From 78c612abc18bed54f8911c84ba6f93eb9f041c31 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Mon, 3 Feb 2020 17:49:04 +0530
Subject: [PATCH 01/83] Update 3.9.rst

---
 Doc/whatsnew/3.9.rst | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/Doc/whatsnew/3.9.rst b/Doc/whatsnew/3.9.rst
index 931f8bf13fbde6..7700d4cc36e0d8 100644
--- a/Doc/whatsnew/3.9.rst
+++ b/Doc/whatsnew/3.9.rst
@@ -216,6 +216,9 @@ Add :func:`math.ulp`: return the value of the least significant bit
 of a float.
 (Contributed by Victor Stinner in :issue:`39310`.)
 
+Add :func:`math.lcm`: return the least common multiple of *a* and *b*.
+(Contributed by Ananthakrishnan in :issue:`39479`.) 
+
 nntplib
 -------
 

From 8300b4e836af5e26a1205e0c5c137bceb56d894b Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Mon, 3 Feb 2020 17:51:59 +0530
Subject: [PATCH 02/83] Update math.rst

---
 Doc/library/math.rst | 9 +++++++++
 1 file changed, 9 insertions(+)

diff --git a/Doc/library/math.rst b/Doc/library/math.rst
index c4c180037f8788..bf2d3401dbeccc 100644
--- a/Doc/library/math.rst
+++ b/Doc/library/math.rst
@@ -136,6 +136,15 @@ Number-theoretic and representation functions
    .. versionadded:: 3.5
 
 
+.. function:: lcm(a, b)
+
+   Return the least common multiple of integers *a* and *b*. If either *a* or 
+   *b* is nonzero,then the value of ``lcm(a, b)`` is the smallest positive 
+   integer that is divisible by both *a* and *b*.``lcm(0, 0)`` returns ``0``.
+
+.. versionadded:: 1.0
+
+
 .. function:: isclose(a, b, *, rel_tol=1e-09, abs_tol=0.0)
 
    Return ``True`` if the values *a* and *b* are close to each other and

From 4c215e8dc1a92e97e1d463c76ea29115ba849f68 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Mon, 3 Feb 2020 17:54:47 +0530
Subject: [PATCH 03/83] Update test_math.py

---
 Lib/test/test_math.py | 43 +++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 43 insertions(+)

diff --git a/Lib/test/test_math.py b/Lib/test/test_math.py
index b3301f6a5cf74f..223061c5eb3fa9 100644
--- a/Lib/test/test_math.py
+++ b/Lib/test/test_math.py
@@ -974,6 +974,49 @@ def __index__(self):
                 with self.assertRaises(TypeError):
                     math.isqrt(value)
 
+     def testlcm(self):
+        lcm = math.lcm
+        self.assertEqual(lcm(0, 0), 0)
+        self.assertEqual(lcm(1, 0), 1)
+        self.assertEqual(lcm(-1, 0), 1)
+        self.assertEqual(lcm(0, 1), 1)
+        self.assertEqual(lcm(0, -1), 1)
+        self.assertEqual(lcm(7, 1), 1)
+        self.assertEqual(lcm(7, -1), 1)
+        self.assertEqual(lcm(-23, 15), 1)
+        self.assertEqual(lcm(120, 84), 12)
+        self.assertEqual(lcm(84, -120), 12)
+        self.assertEqual(lcm(1216342683557601535506311712,
+                             436522681849110124616458784), 32)
+        c = 652560
+        x = 434610456570399902378880679233098819019853229470286994367836600566
+        y = 1064502245825115327754847244914921553977
+        a = x * c
+        b = y * c
+        self.assertEqual(lcm(a, b), c)
+        self.assertEqual(lcm(b, a), c)
+        self.assertEqual(lcm(-a, b), c)
+        self.assertEqual(lcm(b, -a), c)
+        self.assertEqual(lcm(a, -b), c)
+        self.assertEqual(lcm(-b, a), c)
+        self.assertEqual(lcm(-a, -b), c)
+        self.assertEqual(lcm(-b, -a), c)
+        c = 576559230871654959816130551884856912003141446781646602790216406874
+        a = x * c
+        b = y * c
+        self.assertEqual(lcm(a, b), c)
+        self.assertEqual(lcm(b, a), c)
+        self.assertEqual(lcm(-a, b), c)
+        self.assertEqual(lcm(b, -a), c)
+        self.assertEqual(lcm(a, -b), c)
+        self.assertEqual(lcm(-b, a), c)
+        self.assertEqual(lcm(-a, -b), c)
+        self.assertEqual(lcm(-b, -a), c)
+
+        self.assertRaises(TypeError, lcm, 120.0, 84)
+        self.assertRaises(TypeError, lcm, 120, 84.0)
+        self.assertEqual(lcm(MyIndexable(120), MyIndexable(84)), 12)
+        
     def testLdexp(self):
         self.assertRaises(TypeError, math.ldexp)
         self.ftest('ldexp(0,1)', math.ldexp(0,1), 0)

From 5ad99af693d23acedb40d2e1bdab9ebb45300a32 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Mon, 3 Feb 2020 17:57:04 +0530
Subject: [PATCH 04/83] Update mathmodule.c

---
 Modules/mathmodule.c | 73 ++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 73 insertions(+)

diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index f012b51d86698d..3b8a854c1e5c04 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -2016,6 +2016,78 @@ math_factorial(PyObject *module, PyObject *arg)
 }
 
 
+/*[clinic input]
+math.lcm
+
+	x as a: object
+	y as b: object
+    /
+least common multiple of x and y
+[clinic start generated code]*/
+
+static PyObject*
+math_lcm(PyObject*module,PyObject*a,PyObject*b)
+{
+    PyObject * g,*m,*f,*ab;
+    if (PyFloat_Check(a)||PyFloat_Check(b)) {
+    if (PyErr_WarnEx(PyExc_DeprecationWarning,
+                    "lcm() cannot be used with float",
+                    1) < 0)
+        {
+            return NULL;
+        }
+    double dx = PyFloat_AS_DOUBLE((PyFloatObject *)a);
+    double ax=   PyFloat_AS_DOUBLE((PyFloatObject *)b);
+    if (!((Py_IS_FINITE(dx) && dx == floor(dx))||(Py_IS_FINITE(ax) && ax == floor(ax))) 
+		{
+            PyErr_SetString(PyExc_ValueError,
+                            "lcm() only accepts integral values");
+            return NULL;
+        }
+    a=PyNumber_Index(a);
+    if(a==NULL)
+        return NULL;
+    b=PyNumber_Index(b);
+    if (b== NULL)
+        {
+        Py_DECREF(a);
+        return NULL;
+         }
+    g=_PyLong_GCD(a,b);
+    Py_DECREF(a);
+    Py_DECREF(b);
+    if(g==NULL)
+    {
+    Py_DECREF(g);
+    return NULL;
+    }     
+    m=PyNumber_Multiply(a,b);
+    Py_DECREF(a);
+    Py_DECREF(b);
+    if(m==NULL)
+        {
+        Py_DECREF(m);
+        return NULL;
+        }    
+    f=PyNumber_FloorDivide(m,g);
+    Py_DECREF(m);
+    Py_DECREF(g);
+    if(f==NULL)
+         {
+		 Py_DECREF(f);
+        return NULL;
+         }
+    ab=PyNumber_Absolute(f);
+    Py_DECREF(f);
+    if(ab==NULL)
+         {
+		 Py_DECREF(ab);
+        return NULL;
+         }
+    return g;
+}
+
+
 /*[clinic input]
 math.trunc
 
@@ -3335,6 +3407,7 @@ static PyMethodDef math_methods[] = {
     {"asin",            math_asin,      METH_O,         math_asin_doc},
     {"asinh",           math_asinh,     METH_O,         math_asinh_doc},
     {"atan",            math_atan,      METH_O,         math_atan_doc},
+    {"lcm",             math_lcm,       METH_O,         math_lcm_doc},
     {"atan2",           (PyCFunction)(void(*)(void))math_atan2,     METH_FASTCALL,  math_atan2_doc},
     {"atanh",           math_atanh,     METH_O,         math_atanh_doc},
     MATH_CEIL_METHODDEF

From c3731390d19ce02b7f9fefdaf11a0c95c7d77173 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Mon, 3 Feb 2020 18:44:04 +0530
Subject: [PATCH 05/83] Update Doc/library/math.rst

Co-Authored-By: Dong-hee Na <donghee.na92@gmail.com>
---
 Doc/library/math.rst | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Doc/library/math.rst b/Doc/library/math.rst
index bf2d3401dbeccc..c0555df953814a 100644
--- a/Doc/library/math.rst
+++ b/Doc/library/math.rst
@@ -142,7 +142,7 @@ Number-theoretic and representation functions
    *b* is nonzero,then the value of ``lcm(a, b)`` is the smallest positive 
    integer that is divisible by both *a* and *b*.``lcm(0, 0)`` returns ``0``.
 
-.. versionadded:: 1.0
+.. versionadded:: 3.9
 
 
 .. function:: isclose(a, b, *, rel_tol=1e-09, abs_tol=0.0)

From a23ba1451a92d3de8b8b6a9b78a9ff720736e8f6 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Mon, 3 Feb 2020 19:33:42 +0530
Subject: [PATCH 06/83] Update Doc/library/math.rst

Co-Authored-By: Victor Stinner <vstinner@python.org>
---
 Doc/library/math.rst | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Doc/library/math.rst b/Doc/library/math.rst
index c0555df953814a..813803a715a26d 100644
--- a/Doc/library/math.rst
+++ b/Doc/library/math.rst
@@ -139,7 +139,7 @@ Number-theoretic and representation functions
 .. function:: lcm(a, b)
 
    Return the least common multiple of integers *a* and *b*. If either *a* or 
-   *b* is nonzero,then the value of ``lcm(a, b)`` is the smallest positive 
+   *b* is nonzero, then the value of ``lcm(a, b)`` is the smallest positive 
    integer that is divisible by both *a* and *b*.``lcm(0, 0)`` returns ``0``.
 
 .. versionadded:: 3.9

From b540fc70850dd432031a17830e351e210c672a03 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Mon, 3 Feb 2020 19:34:22 +0530
Subject: [PATCH 07/83] Update Lib/test/test_math.py

Co-Authored-By: Victor Stinner <vstinner@python.org>
---
 Lib/test/test_math.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Lib/test/test_math.py b/Lib/test/test_math.py
index 223061c5eb3fa9..3ef452b37bb1c0 100644
--- a/Lib/test/test_math.py
+++ b/Lib/test/test_math.py
@@ -974,7 +974,7 @@ def __index__(self):
                 with self.assertRaises(TypeError):
                     math.isqrt(value)
 
-     def testlcm(self):
+     def test_lcm(self):
         lcm = math.lcm
         self.assertEqual(lcm(0, 0), 0)
         self.assertEqual(lcm(1, 0), 1)

From 13be573d514f71a4356dae6380f77652bb1a0793 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Mon, 3 Feb 2020 19:35:00 +0530
Subject: [PATCH 08/83] Update Doc/library/math.rst

Co-Authored-By: Victor Stinner <vstinner@python.org>
---
 Doc/library/math.rst | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Doc/library/math.rst b/Doc/library/math.rst
index 813803a715a26d..101e0f2db54487 100644
--- a/Doc/library/math.rst
+++ b/Doc/library/math.rst
@@ -140,7 +140,7 @@ Number-theoretic and representation functions
 
    Return the least common multiple of integers *a* and *b*. If either *a* or 
    *b* is nonzero, then the value of ``lcm(a, b)`` is the smallest positive 
-   integer that is divisible by both *a* and *b*.``lcm(0, 0)`` returns ``0``.
+   integer that is divisible by both *a* and *b*. ``lcm(0, 0)`` returns ``0``.
 
 .. versionadded:: 3.9
 

From a3a36ab73664abe989d5b07feec7e8c501b26424 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Mon, 3 Feb 2020 20:00:49 +0530
Subject: [PATCH 09/83] Update mathmodule.c

---
 Modules/mathmodule.c | 70 ++++++++++++++++++++------------------------
 1 file changed, 32 insertions(+), 38 deletions(-)

diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index 3b8a854c1e5c04..c566f51d46b9b1 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -2026,64 +2026,58 @@ least common multiple of x and y
 [clinic start generated code]*/
 
 static PyObject*
-math_lcm(PyObject*module,PyObject*a,PyObject*b)
+math_lcm(PyObject*module, PyObject*a, PyObject*b)
 {
     PyObject * g,*m,*f,*ab;
-    if (PyFloat_Check(a)||PyFloat_Check(b)) {
-    if (PyErr_WarnEx(PyExc_DeprecationWarning,
-                    "lcm() cannot be used with float",
-                    1) < 0)
-        {
-            return NULL;
-        }
-    double dx = PyFloat_AS_DOUBLE((PyFloatObject *)a);
-    double ax=   PyFloat_AS_DOUBLE((PyFloatObject *)b);
-    if (!((Py_IS_FINITE(dx) && dx == floor(dx))||(Py_IS_FINITE(ax) && ax == floor(ax))) 
-		{
-            PyErr_SetString(PyExc_ValueError,
-                            "lcm() only accepts integral values");
-            return NULL;
-        }
+	
     a=PyNumber_Index(a);
-    if(a==NULL)
+	
+    if (a == NULL) {
         return NULL;
+    }
+	
     b=PyNumber_Index(b);
-    if (b== NULL)
-        {
+	
+    if (b== NULL) {
         Py_DECREF(a);
         return NULL;
-         }
-    g=_PyLong_GCD(a,b);
+    }
+	
+    g=_PyLong_GCD(a, b);
     Py_DECREF(a);
     Py_DECREF(b);
-    if(g==NULL)
-    {
-    Py_DECREF(g);
-    return NULL;
+	
+    if (g==NULL) {
+        Py_DECREF(g);
+        return NULL;
     }     
-    m=PyNumber_Multiply(a,b);
+	
+    m=PyNumber_Multiply(a, b);
     Py_DECREF(a);
     Py_DECREF(b);
-    if(m==NULL)
-        {
+	
+    if (m==NULL) {
         Py_DECREF(m);
         return NULL;
-        }    
-    f=PyNumber_FloorDivide(m,g);
+     }    
+	
+    f=PyNumber_FloorDivide(m, g);
     Py_DECREF(m);
     Py_DECREF(g);
-    if(f==NULL)
-         {
-		 Py_DECREF(f);
+	
+    if (f==NULL) {
+        Py_DECREF(f);
         return NULL;
-         }
+     }
+	
     ab=PyNumber_Absolute(f);
     Py_DECREF(f);
-    if(ab==NULL)
-         {
-		 Py_DECREF(ab);
+	
+    if (ab==NULL) {
+        Py_DECREF(ab);
         return NULL;
-         }
+    }
+	
     return g;
 }
 

From 34efffa0ade6845235227426b2e415dff8a0a7a6 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Mon, 3 Feb 2020 21:16:01 +0530
Subject: [PATCH 10/83] Update test_math.py

---
 Lib/test/test_math.py | 37 ++++++++++++++-----------------------
 1 file changed, 14 insertions(+), 23 deletions(-)

diff --git a/Lib/test/test_math.py b/Lib/test/test_math.py
index 3ef452b37bb1c0..41c04e896fc586 100644
--- a/Lib/test/test_math.py
+++ b/Lib/test/test_math.py
@@ -988,31 +988,22 @@ def test_lcm(self):
         self.assertEqual(lcm(84, -120), 12)
         self.assertEqual(lcm(1216342683557601535506311712,
                              436522681849110124616458784), 32)
-        c = 652560
         x = 434610456570399902378880679233098819019853229470286994367836600566
         y = 1064502245825115327754847244914921553977
-        a = x * c
-        b = y * c
-        self.assertEqual(lcm(a, b), c)
-        self.assertEqual(lcm(b, a), c)
-        self.assertEqual(lcm(-a, b), c)
-        self.assertEqual(lcm(b, -a), c)
-        self.assertEqual(lcm(a, -b), c)
-        self.assertEqual(lcm(-b, a), c)
-        self.assertEqual(lcm(-a, -b), c)
-        self.assertEqual(lcm(-b, -a), c)
-        c = 576559230871654959816130551884856912003141446781646602790216406874
-        a = x * c
-        b = y * c
-        self.assertEqual(lcm(a, b), c)
-        self.assertEqual(lcm(b, a), c)
-        self.assertEqual(lcm(-a, b), c)
-        self.assertEqual(lcm(b, -a), c)
-        self.assertEqual(lcm(a, -b), c)
-        self.assertEqual(lcm(-b, a), c)
-        self.assertEqual(lcm(-a, -b), c)
-        self.assertEqual(lcm(-b, -a), c)
-
+        
+        for c in (652560,
+                  576559230871654959816130551884856912003141446781646602790216406874,
+                  ):
+            a = x * c
+            b = y * c
+            self.assertEqual(lcm(a, b), c)
+            self.assertEqual(lcm(b, a), c)
+            self.assertEqual(lcm(-a, b), c)
+            self.assertEqual(lcm(b, -a), c)
+            self.assertEqual(lcm(a, -b), c)
+            self.assertEqual(lcm(-b, a), c)
+            self.assertEqual(lcm(-a, -b), c)
+            self.assertEqual(lcm(-b, -a), c)
         self.assertRaises(TypeError, lcm, 120.0, 84)
         self.assertRaises(TypeError, lcm, 120, 84.0)
         self.assertEqual(lcm(MyIndexable(120), MyIndexable(84)), 12)

From e42b00c36177af994a877b0588678544ea6932d6 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Mon, 3 Feb 2020 22:38:40 +0530
Subject: [PATCH 11/83] Update mathmodule.c

---
 Modules/mathmodule.c | 26 +++++++++++++-------------
 1 file changed, 13 insertions(+), 13 deletions(-)

diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index c566f51d46b9b1..60a697ad1950de 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -2026,54 +2026,54 @@ least common multiple of x and y
 [clinic start generated code]*/
 
 static PyObject*
-math_lcm(PyObject*module, PyObject*a, PyObject*b)
+math_lcm(PyObject *module, PyObject *a, PyObject *b)
 {
-    PyObject * g,*m,*f,*ab;
+    PyObject*g,*m,*f,*ab;
 	
-    a=PyNumber_Index(a);
+    a = PyNumber_Index(a);
 	
     if (a == NULL) {
         return NULL;
     }
 	
-    b=PyNumber_Index(b);
+    b = PyNumber_Index(b);
 	
-    if (b== NULL) {
+    if (b == NULL) {
         Py_DECREF(a);
         return NULL;
     }
 	
-    g=_PyLong_GCD(a, b);
+    g = _PyLong_GCD(a, b);
     Py_DECREF(a);
     Py_DECREF(b);
 	
-    if (g==NULL) {
+    if (g == NULL) {
         Py_DECREF(g);
         return NULL;
     }     
 	
-    m=PyNumber_Multiply(a, b);
+    m = PyNumber_Multiply(a, b);
     Py_DECREF(a);
     Py_DECREF(b);
 	
-    if (m==NULL) {
+    if (m == NULL) {
         Py_DECREF(m);
         return NULL;
      }    
 	
-    f=PyNumber_FloorDivide(m, g);
+    f = PyNumber_FloorDivide(m, g);
     Py_DECREF(m);
     Py_DECREF(g);
 	
-    if (f==NULL) {
+    if (f == NULL) {
         Py_DECREF(f);
         return NULL;
      }
 	
-    ab=PyNumber_Absolute(f);
+    ab = PyNumber_Absolute(f);
     Py_DECREF(f);
 	
-    if (ab==NULL) {
+    if (ab == NULL) {
         Py_DECREF(ab);
         return NULL;
     }

From 091c4a6ab8521695ec563ae34a676d062e74d6c5 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Mon, 3 Feb 2020 22:40:48 +0530
Subject: [PATCH 12/83] Update mathmodule.c

---
 Modules/mathmodule.c | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index 60a697ad1950de..6bfa4e244fedf2 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -2028,7 +2028,7 @@ least common multiple of x and y
 static PyObject*
 math_lcm(PyObject *module, PyObject *a, PyObject *b)
 {
-    PyObject*g,*m,*f,*ab;
+    PyObject *g, *m, *f, *ab;
 	
     a = PyNumber_Index(a);
 	

From 99b1364711c248a7395d820f6908b62c4550cc26 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Mon, 3 Feb 2020 23:07:44 +0530
Subject: [PATCH 13/83] Update mathmodule.c

---
 Modules/mathmodule.c | 7 +++++++
 1 file changed, 7 insertions(+)

diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index 6bfa4e244fedf2..2e05515589339f 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -2081,6 +2081,13 @@ math_lcm(PyObject *module, PyObject *a, PyObject *b)
     return g;
 }
 
+PyDoc_STRVAR(math_lcm_doc,
+"lcm($module, x, y, /)\n"
+"--\n"
+"\n"
+	     
+"least common multiple of x and y");
+
 
 /*[clinic input]
 math.trunc

From a5d89b5ea1b8f3f053033120ac0926ec823684ee Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Mon, 3 Feb 2020 23:12:20 +0530
Subject: [PATCH 14/83] Update math.rst

---
 Doc/library/math.rst | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Doc/library/math.rst b/Doc/library/math.rst
index 101e0f2db54487..5d5d2447bdc050 100644
--- a/Doc/library/math.rst
+++ b/Doc/library/math.rst
@@ -142,7 +142,7 @@ Number-theoretic and representation functions
    *b* is nonzero, then the value of ``lcm(a, b)`` is the smallest positive 
    integer that is divisible by both *a* and *b*. ``lcm(0, 0)`` returns ``0``.
 
-.. versionadded:: 3.9
+   .. versionadded:: 3.9
 
 
 .. function:: isclose(a, b, *, rel_tol=1e-09, abs_tol=0.0)

From 7823c12f12ffd07f59bca0fa0bcb392af6103e33 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Mon, 3 Feb 2020 23:26:00 +0530
Subject: [PATCH 15/83] Update math.rst

---
 Doc/library/math.rst | 6 ++++--
 1 file changed, 4 insertions(+), 2 deletions(-)

diff --git a/Doc/library/math.rst b/Doc/library/math.rst
index 5d5d2447bdc050..e4a802fbd29d69 100644
--- a/Doc/library/math.rst
+++ b/Doc/library/math.rst
@@ -139,8 +139,10 @@ Number-theoretic and representation functions
 .. function:: lcm(a, b)
 
    Return the least common multiple of integers *a* and *b*. If either *a* or 
-   *b* is nonzero, then the value of ``lcm(a, b)`` is the smallest positive 
-   integer that is divisible by both *a* and *b*. ``lcm(0, 0)`` returns ``0``.
+   *b* is nonzero,then the value of ``lcm(a, b)`` is the smallest positive 
+   integer that is divisible by both *a* and *b*.``lcm(0, 0)`` returns ``0``.
+   ``lcm(a, b)`` returns *g* by calling ``gcd(a, b)``.
+   Thus ``lcm(a, b)=abs(a // gcd(a, b) * b)``.
 
    .. versionadded:: 3.9
 

From ce474a82648bdeb0b46b26c3b95b1ecf34d48a7c Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Mon, 3 Feb 2020 23:29:45 +0530
Subject: [PATCH 16/83] Update Doc/library/math.rst

Co-Authored-By: Victor Stinner <vstinner@python.org>
---
 Doc/library/math.rst | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Doc/library/math.rst b/Doc/library/math.rst
index e4a802fbd29d69..dbfb69dc9e6c10 100644
--- a/Doc/library/math.rst
+++ b/Doc/library/math.rst
@@ -140,7 +140,7 @@ Number-theoretic and representation functions
 
    Return the least common multiple of integers *a* and *b*. If either *a* or 
    *b* is nonzero,then the value of ``lcm(a, b)`` is the smallest positive 
-   integer that is divisible by both *a* and *b*.``lcm(0, 0)`` returns ``0``.
+   integer that is divisible by both *a* and *b*. ``lcm(0, 0)`` returns ``0``.
    ``lcm(a, b)`` returns *g* by calling ``gcd(a, b)``.
    Thus ``lcm(a, b)=abs(a // gcd(a, b) * b)``.
 

From aa9abb73bb3e5224a1a7987e9fb21dfd28a2e164 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Mon, 3 Feb 2020 23:31:29 +0530
Subject: [PATCH 17/83] Update Doc/library/math.rst

Co-Authored-By: Victor Stinner <vstinner@python.org>
---
 Doc/library/math.rst | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Doc/library/math.rst b/Doc/library/math.rst
index dbfb69dc9e6c10..d6b5353aac7fa1 100644
--- a/Doc/library/math.rst
+++ b/Doc/library/math.rst
@@ -139,7 +139,7 @@ Number-theoretic and representation functions
 .. function:: lcm(a, b)
 
    Return the least common multiple of integers *a* and *b*. If either *a* or 
-   *b* is nonzero,then the value of ``lcm(a, b)`` is the smallest positive 
+   *b* is nonzero, then the value of ``lcm(a, b)`` is the smallest positive 
    integer that is divisible by both *a* and *b*. ``lcm(0, 0)`` returns ``0``.
    ``lcm(a, b)`` returns *g* by calling ``gcd(a, b)``.
    Thus ``lcm(a, b)=abs(a // gcd(a, b) * b)``.

From 79bf932d9a437783460a6788c416d4a17750e3db Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Mon, 3 Feb 2020 23:33:18 +0530
Subject: [PATCH 18/83] Update math.rst

---
 Doc/library/math.rst | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Doc/library/math.rst b/Doc/library/math.rst
index d6b5353aac7fa1..3a4839d617724c 100644
--- a/Doc/library/math.rst
+++ b/Doc/library/math.rst
@@ -142,7 +142,7 @@ Number-theoretic and representation functions
    *b* is nonzero, then the value of ``lcm(a, b)`` is the smallest positive 
    integer that is divisible by both *a* and *b*. ``lcm(0, 0)`` returns ``0``.
    ``lcm(a, b)`` returns *g* by calling ``gcd(a, b)``.
-   Thus ``lcm(a, b)=abs(a // gcd(a, b) * b)``.
+   Thus ``lcm(a, b) = abs(a // gcd(a, b) * b)``.
 
    .. versionadded:: 3.9
 

From 972f8e6d20c7c62d7d5e82c828f11d0fd2b9edf4 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Tue, 4 Feb 2020 19:05:05 +0530
Subject: [PATCH 19/83] Update math.rst

---
 Doc/library/math.rst | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Doc/library/math.rst b/Doc/library/math.rst
index 3a4839d617724c..50e9dd9a319e5e 100644
--- a/Doc/library/math.rst
+++ b/Doc/library/math.rst
@@ -138,9 +138,9 @@ Number-theoretic and representation functions
 
 .. function:: lcm(a, b)
 
-   Return the least common multiple of integers *a* and *b*. If either *a* or 
+   Return the least common multiple of integers *a* and *b*.  If either *a* or
    *b* is nonzero, then the value of ``lcm(a, b)`` is the smallest positive 
-   integer that is divisible by both *a* and *b*. ``lcm(0, 0)`` returns ``0``.
+   integer that is divisible by both *a* and *b*.  ``lcm(0, 0)`` returns ``0``.
    ``lcm(a, b)`` returns *g* by calling ``gcd(a, b)``.
    Thus ``lcm(a, b) = abs(a // gcd(a, b) * b)``.
 

From 75988952ee8ed082ca64bde7de948ae79b8f9ed6 Mon Sep 17 00:00:00 2001
From: "blurb-it[bot]" <43283697+blurb-it[bot]@users.noreply.github.com>
Date: Tue, 4 Feb 2020 13:47:18 +0000
Subject: [PATCH 20/83] =?UTF-8?q?=F0=9F=93=9C=F0=9F=A4=96=20Added=20by=20b?=
 =?UTF-8?q?lurb=5Fit.?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 .../NEWS.d/next/Library/2020-02-04-13-47-16.bpo-39479.BN_mM9.rst | 1 +
 1 file changed, 1 insertion(+)
 create mode 100644 Misc/NEWS.d/next/Library/2020-02-04-13-47-16.bpo-39479.BN_mM9.rst

diff --git a/Misc/NEWS.d/next/Library/2020-02-04-13-47-16.bpo-39479.BN_mM9.rst b/Misc/NEWS.d/next/Library/2020-02-04-13-47-16.bpo-39479.BN_mM9.rst
new file mode 100644
index 00000000000000..cf888d71417f0a
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2020-02-04-13-47-16.bpo-39479.BN_mM9.rst
@@ -0,0 +1 @@
+Add `math.lcm()` function: Least Common Multiple.
\ No newline at end of file

From 42669da079a7598779253d43d0c22b3ec0ffacfe Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Tue, 4 Feb 2020 19:26:12 +0530
Subject: [PATCH 21/83] Update math.rst

---
 Doc/library/math.rst | 4 +---
 1 file changed, 1 insertion(+), 3 deletions(-)

diff --git a/Doc/library/math.rst b/Doc/library/math.rst
index 50e9dd9a319e5e..17ae31e96b3a15 100644
--- a/Doc/library/math.rst
+++ b/Doc/library/math.rst
@@ -141,9 +141,7 @@ Number-theoretic and representation functions
    Return the least common multiple of integers *a* and *b*.  If either *a* or
    *b* is nonzero, then the value of ``lcm(a, b)`` is the smallest positive 
    integer that is divisible by both *a* and *b*.  ``lcm(0, 0)`` returns ``0``.
-   ``lcm(a, b)`` returns *g* by calling ``gcd(a, b)``.
-   Thus ``lcm(a, b) = abs(a // gcd(a, b) * b)``.
-
+  
    .. versionadded:: 3.9
 
 

From 4ee5b20da323b104dba8f3d39d062511a3393f6f Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Tue, 4 Feb 2020 19:36:33 +0530
Subject: [PATCH 22/83] Update mathmodule.c

---
 Modules/mathmodule.c | 11 -----------
 1 file changed, 11 deletions(-)

diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index 2e05515589339f..58e0f4a31f96e2 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -2031,48 +2031,37 @@ math_lcm(PyObject *module, PyObject *a, PyObject *b)
     PyObject *g, *m, *f, *ab;
 	
     a = PyNumber_Index(a);
-	
     if (a == NULL) {
         return NULL;
     }
-	
     b = PyNumber_Index(b);
-	
     if (b == NULL) {
         Py_DECREF(a);
         return NULL;
     }
-	
     g = _PyLong_GCD(a, b);
     Py_DECREF(a);
     Py_DECREF(b);
-	
     if (g == NULL) {
         Py_DECREF(g);
         return NULL;
     }     
-	
     m = PyNumber_Multiply(a, b);
     Py_DECREF(a);
     Py_DECREF(b);
-	
     if (m == NULL) {
         Py_DECREF(m);
         return NULL;
      }    
-	
     f = PyNumber_FloorDivide(m, g);
     Py_DECREF(m);
     Py_DECREF(g);
-	
     if (f == NULL) {
         Py_DECREF(f);
         return NULL;
      }
-	
     ab = PyNumber_Absolute(f);
     Py_DECREF(f);
-	
     if (ab == NULL) {
         Py_DECREF(ab);
         return NULL;

From 97a54dbec251e96fe3895ffac2855e92d147cfb1 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Tue, 4 Feb 2020 20:01:30 +0530
Subject: [PATCH 23/83] Update mathmodule.c

---
 Modules/mathmodule.c | 12 +++++-------
 1 file changed, 5 insertions(+), 7 deletions(-)

diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index 58e0f4a31f96e2..ef1ca363ba3599 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -2040,22 +2040,20 @@ math_lcm(PyObject *module, PyObject *a, PyObject *b)
         return NULL;
     }
     g = _PyLong_GCD(a, b);
-    Py_DECREF(a);
-    Py_DECREF(b);
     if (g == NULL) {
         Py_DECREF(g);
         return NULL;
     }     
-    m = PyNumber_Multiply(a, b);
+    m = PyNumber_Multiply(g, a);
+    Py_DECREF(g);
     Py_DECREF(a);
-    Py_DECREF(b);
     if (m == NULL) {
         Py_DECREF(m);
         return NULL;
      }    
-    f = PyNumber_FloorDivide(m, g);
+    f = PyNumber_FloorDivide(a, m);
+    Py_DECREF(a);
     Py_DECREF(m);
-    Py_DECREF(g);
     if (f == NULL) {
         Py_DECREF(f);
         return NULL;
@@ -2067,7 +2065,7 @@ math_lcm(PyObject *module, PyObject *a, PyObject *b)
         return NULL;
     }
 	
-    return g;
+    return ab;
 }
 
 PyDoc_STRVAR(math_lcm_doc,

From 4072d9238a59402170e00cad9ea44f0c2db1db5d Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Tue, 4 Feb 2020 20:03:03 +0530
Subject: [PATCH 24/83] Update math.rst

---
 Doc/library/math.rst | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Doc/library/math.rst b/Doc/library/math.rst
index 17ae31e96b3a15..e8f087b8af6c5a 100644
--- a/Doc/library/math.rst
+++ b/Doc/library/math.rst
@@ -138,7 +138,7 @@ Number-theoretic and representation functions
 
 .. function:: lcm(a, b)
 
-   Return the least common multiple of integers *a* and *b*.  If either *a* or
+   Return the least common multiple of integers *a* and *b*.  If both *a* or
    *b* is nonzero, then the value of ``lcm(a, b)`` is the smallest positive 
    integer that is divisible by both *a* and *b*.  ``lcm(0, 0)`` returns ``0``.
   

From 38fa5ed663e59f83749e005eca460ae898afc8c8 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Tue, 4 Feb 2020 20:05:46 +0530
Subject: [PATCH 25/83] Update math.rst

---
 Doc/library/math.rst | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Doc/library/math.rst b/Doc/library/math.rst
index e8f087b8af6c5a..88384ff02da2de 100644
--- a/Doc/library/math.rst
+++ b/Doc/library/math.rst
@@ -140,7 +140,7 @@ Number-theoretic and representation functions
 
    Return the least common multiple of integers *a* and *b*.  If both *a* or
    *b* is nonzero, then the value of ``lcm(a, b)`` is the smallest positive 
-   integer that is divisible by both *a* and *b*.  ``lcm(0, 0)`` returns ``0``.
+   integer that is multiple of both *a* and *b*.  ``lcm(0, 0)`` returns ``0``.
   
    .. versionadded:: 3.9
 

From e616c7405043f447a3bd2ef6e18377edcf895696 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Tue, 4 Feb 2020 21:47:29 +0530
Subject: [PATCH 26/83] Update test_math.py

---
 Lib/test/test_math.py | 60 +++++++++++++++++++++++++------------------
 1 file changed, 35 insertions(+), 25 deletions(-)

diff --git a/Lib/test/test_math.py b/Lib/test/test_math.py
index 41c04e896fc586..13fc5963248f93 100644
--- a/Lib/test/test_math.py
+++ b/Lib/test/test_math.py
@@ -977,36 +977,46 @@ def __index__(self):
      def test_lcm(self):
         lcm = math.lcm
         self.assertEqual(lcm(0, 0), 0)
-        self.assertEqual(lcm(1, 0), 1)
-        self.assertEqual(lcm(-1, 0), 1)
-        self.assertEqual(lcm(0, 1), 1)
-        self.assertEqual(lcm(0, -1), 1)
-        self.assertEqual(lcm(7, 1), 1)
-        self.assertEqual(lcm(7, -1), 1)
-        self.assertEqual(lcm(-23, 15), 1)
-        self.assertEqual(lcm(120, 84), 12)
-        self.assertEqual(lcm(84, -120), 12)
+        self.assertEqual(lcm(1, 0), 0)
+        self.assertEqual(lcm(-1, 0), 0)
+        self.assertEqual(lcm(0, 1), 0)
+        self.assertEqual(lcm(0, -1), 0)
+        self.assertEqual(lcm(7, 1), 7)
+        self.assertEqual(lcm(7, -1), 7)
+        self.assertEqual(lcm(-23, 15), 345)
+        self.assertEqual(lcm(120, 84), 840)
+        self.assertEqual(lcm(84, -120), 840)
         self.assertEqual(lcm(1216342683557601535506311712,
-                             436522681849110124616458784), 32)
+                             436522681849110124616458784),
+                             16592536571065866494401400422922201534178938447014944)
+        c = 652560
         x = 434610456570399902378880679233098819019853229470286994367836600566
         y = 1064502245825115327754847244914921553977
-        
-        for c in (652560,
-                  576559230871654959816130551884856912003141446781646602790216406874,
-                  ):
-            a = x * c
-            b = y * c
-            self.assertEqual(lcm(a, b), c)
-            self.assertEqual(lcm(b, a), c)
-            self.assertEqual(lcm(-a, b), c)
-            self.assertEqual(lcm(b, -a), c)
-            self.assertEqual(lcm(a, -b), c)
-            self.assertEqual(lcm(-b, a), c)
-            self.assertEqual(lcm(-a, -b), c)
-            self.assertEqual(lcm(-b, -a), c)
+        a = x * c
+        b = y * c
+        d=301902842746995509648393721908560577474971578942451106771953796961736341663923782888922697319520284637980813920 652560
+        self.assertEqual(lcm(a, b), d)
+        self.assertEqual(lcm(b, a), d)
+        self.assertEqual(lcm(-a, b), d)
+        self.assertEqual(lcm(b, -a), d)
+        self.assertEqual(lcm(a, -b), d)
+        self.assertEqual(lcm(-b, a), d)
+        self.assertEqual(lcm(-a, -b), d)
+        self.assertEqual(lcm(-b, -a), d)
+	    e=266741557576581350556796933681042612304362158146595254541737503518981783311378696068765001186892238054415825401472091853286591831877639677191947722648985671425215285050268
+	    c = 576559230871654959816130551884856912003141446781646602790216406874
+        a = x * c
+        b = y * c
+        self.assertEqual(lcm(a, b), e)
+        self.assertEqual(lcm(b, a), e)
+        self.assertEqual(lcm(-a, b), e)
+        self.assertEqual(lcm(b, -a), e)
+        self.assertEqual(lcm(a, -b), e)
+        self.assertEqual(lcm(-b, a), e)
+        self.assertEqual(lcm(-a, -b), e)
+        self.assertEqual(lcm(-b, -a), e)
         self.assertRaises(TypeError, lcm, 120.0, 84)
         self.assertRaises(TypeError, lcm, 120, 84.0)
-        self.assertEqual(lcm(MyIndexable(120), MyIndexable(84)), 12)
         
     def testLdexp(self):
         self.assertRaises(TypeError, math.ldexp)

From fbb064a3c03520bbd67fbadd658fa9c72e939ecd Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Tue, 4 Feb 2020 22:08:40 +0530
Subject: [PATCH 27/83] Update mathmodule.c

---
 Modules/mathmodule.c | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index ef1ca363ba3599..b5806645d4bd8d 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -2047,6 +2047,7 @@ math_lcm(PyObject *module, PyObject *a, PyObject *b)
     m = PyNumber_Multiply(g, a);
     Py_DECREF(g);
     Py_DECREF(a);
+    Py_DECREF(g);
     if (m == NULL) {
         Py_DECREF(m);
         return NULL;
@@ -2054,12 +2055,14 @@ math_lcm(PyObject *module, PyObject *a, PyObject *b)
     f = PyNumber_FloorDivide(a, m);
     Py_DECREF(a);
     Py_DECREF(m);
+    Py_DECREF(m);
     if (f == NULL) {
         Py_DECREF(f);
         return NULL;
      }
     ab = PyNumber_Absolute(f);
     Py_DECREF(f);
+    Py_DECREF(f);
     if (ab == NULL) {
         Py_DECREF(ab);
         return NULL;

From a72f5ddda8ad868169e9a8d61ced2ae28eb57c8f Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Tue, 4 Feb 2020 22:50:32 +0530
Subject: [PATCH 28/83] Update mathmodule.c

---
 Modules/mathmodule.c | 18 ++++++++----------
 1 file changed, 8 insertions(+), 10 deletions(-)

diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index b5806645d4bd8d..a96da7539c1e1d 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -2041,30 +2041,28 @@ math_lcm(PyObject *module, PyObject *a, PyObject *b)
     }
     g = _PyLong_GCD(a, b);
     if (g == NULL) {
-        Py_DECREF(g);
+        Py_DECREF(a);
+	Py_DECREF(b);
         return NULL;
     }     
     m = PyNumber_Multiply(g, a);
     Py_DECREF(g);
-    Py_DECREF(a);
-    Py_DECREF(g);
     if (m == NULL) {
-        Py_DECREF(m);
+        Py_DECREF(g);
+	Py_DECREF(a);
         return NULL;
      }    
     f = PyNumber_FloorDivide(a, m);
-    Py_DECREF(a);
-    Py_DECREF(m);
     Py_DECREF(m);
     if (f == NULL) {
-        Py_DECREF(f);
+        Py_DECREF(a);
+        Py_DECREF(m);
         return NULL;
      }
     ab = PyNumber_Absolute(f);
-    Py_DECREF(f);
-    Py_DECREF(f);
+    Py_DECREF(m);
     if (ab == NULL) {
-        Py_DECREF(ab);
+        Py_DECREF(f);
         return NULL;
     }
 	

From 049d867a72497e828ac46ce33320f7d4e948b1d1 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Tue, 4 Feb 2020 22:51:50 +0530
Subject: [PATCH 29/83] Update Lib/test/test_math.py

Co-Authored-By: Serhiy Storchaka <storchaka@gmail.com>
---
 Lib/test/test_math.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Lib/test/test_math.py b/Lib/test/test_math.py
index 13fc5963248f93..c7cfc333e65b74 100644
--- a/Lib/test/test_math.py
+++ b/Lib/test/test_math.py
@@ -994,7 +994,7 @@ def test_lcm(self):
         y = 1064502245825115327754847244914921553977
         a = x * c
         b = y * c
-        d=301902842746995509648393721908560577474971578942451106771953796961736341663923782888922697319520284637980813920 652560
+        d = x * y * c
         self.assertEqual(lcm(a, b), d)
         self.assertEqual(lcm(b, a), d)
         self.assertEqual(lcm(-a, b), d)

From 6ed80744fbba4240690002326b76f0efc26b0034 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Tue, 4 Feb 2020 22:57:48 +0530
Subject: [PATCH 30/83] Update test_math.py

---
 Lib/test/test_math.py | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/Lib/test/test_math.py b/Lib/test/test_math.py
index c7cfc333e65b74..e6922f43c783c3 100644
--- a/Lib/test/test_math.py
+++ b/Lib/test/test_math.py
@@ -1002,11 +1002,11 @@ def test_lcm(self):
         self.assertEqual(lcm(a, -b), d)
         self.assertEqual(lcm(-b, a), d)
         self.assertEqual(lcm(-a, -b), d)
-        self.assertEqual(lcm(-b, -a), d)
-	    e=266741557576581350556796933681042612304362158146595254541737503518981783311378696068765001186892238054415825401472091853286591831877639677191947722648985671425215285050268
-	    c = 576559230871654959816130551884856912003141446781646602790216406874
+        self.assertEqual(lcm(-b, -a), d)    
+	c = 576559230871654959816130551884856912003141446781646602790216406874
         a = x * c
         b = y * c
+	e = x * y * c
         self.assertEqual(lcm(a, b), e)
         self.assertEqual(lcm(b, a), e)
         self.assertEqual(lcm(-a, b), e)

From e18e43b86e59ced9b489586217451fde13dac729 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Tue, 4 Feb 2020 23:22:59 +0530
Subject: [PATCH 31/83] Update mathmodule.c

---
 Modules/mathmodule.c | 16 +++++-----------
 1 file changed, 5 insertions(+), 11 deletions(-)

diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index a96da7539c1e1d..a88d55062b4c10 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -2042,39 +2042,33 @@ math_lcm(PyObject *module, PyObject *a, PyObject *b)
     g = _PyLong_GCD(a, b);
     if (g == NULL) {
         Py_DECREF(a);
-	Py_DECREF(b);
+        Py_DECREF(b);
         return NULL;
     }     
     m = PyNumber_Multiply(g, a);
     Py_DECREF(g);
     if (m == NULL) {
         Py_DECREF(g);
-	Py_DECREF(a);
+        Py_DECREF(a);
         return NULL;
-     }    
+    }    
     f = PyNumber_FloorDivide(a, m);
     Py_DECREF(m);
     if (f == NULL) {
         Py_DECREF(a);
         Py_DECREF(m);
         return NULL;
-     }
+    }
     ab = PyNumber_Absolute(f);
     Py_DECREF(m);
     if (ab == NULL) {
         Py_DECREF(f);
         return NULL;
     }
-	
     return ab;
 }
 
-PyDoc_STRVAR(math_lcm_doc,
-"lcm($module, x, y, /)\n"
-"--\n"
-"\n"
-	     
-"least common multiple of x and y");
+
 
 
 /*[clinic input]

From 4e3c1cdbfa914eae2fe51a01091060df9fcd5e6c Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Wed, 5 Feb 2020 00:41:06 +0530
Subject: [PATCH 32/83] Update test_math.py

---
 Lib/test/test_math.py | 38 ++++++++++++++------------------------
 1 file changed, 14 insertions(+), 24 deletions(-)

diff --git a/Lib/test/test_math.py b/Lib/test/test_math.py
index e6922f43c783c3..2c6415dbf57c65 100644
--- a/Lib/test/test_math.py
+++ b/Lib/test/test_math.py
@@ -989,32 +989,22 @@ def test_lcm(self):
         self.assertEqual(lcm(1216342683557601535506311712,
                              436522681849110124616458784),
                              16592536571065866494401400422922201534178938447014944)
-        c = 652560
         x = 434610456570399902378880679233098819019853229470286994367836600566
         y = 1064502245825115327754847244914921553977
-        a = x * c
-        b = y * c
-        d = x * y * c
-        self.assertEqual(lcm(a, b), d)
-        self.assertEqual(lcm(b, a), d)
-        self.assertEqual(lcm(-a, b), d)
-        self.assertEqual(lcm(b, -a), d)
-        self.assertEqual(lcm(a, -b), d)
-        self.assertEqual(lcm(-b, a), d)
-        self.assertEqual(lcm(-a, -b), d)
-        self.assertEqual(lcm(-b, -a), d)    
-	c = 576559230871654959816130551884856912003141446781646602790216406874
-        a = x * c
-        b = y * c
-	e = x * y * c
-        self.assertEqual(lcm(a, b), e)
-        self.assertEqual(lcm(b, a), e)
-        self.assertEqual(lcm(-a, b), e)
-        self.assertEqual(lcm(b, -a), e)
-        self.assertEqual(lcm(a, -b), e)
-        self.assertEqual(lcm(-b, a), e)
-        self.assertEqual(lcm(-a, -b), e)
-        self.assertEqual(lcm(-b, -a), e)
+        
+        for c in (652560,
+                  576559230871654959816130551884856912003141446781646602790216406874)
+            a = x * c
+            b = y * c
+            d = x * y * c
+            self.assertEqual(lcm(a, b), d)
+            self.assertEqual(lcm(b, a), d)
+            self.assertEqual(lcm(-a, b), d)
+            self.assertEqual(lcm(b, -a), d)
+            self.assertEqual(lcm(a, -b), d)
+            self.assertEqual(lcm(-b, a), d)
+            self.assertEqual(lcm(-a, -b), d)
+            self.assertEqual(lcm(-b, -a), d)    
         self.assertRaises(TypeError, lcm, 120.0, 84)
         self.assertRaises(TypeError, lcm, 120, 84.0)
         

From d8b03f98b33dbdacde145c29f8eccb736fdc4c4e Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Wed, 5 Feb 2020 00:44:11 +0530
Subject: [PATCH 33/83] Update mathmodule.c

---
 Modules/mathmodule.c | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index a88d55062b4c10..8cd9d94964c38a 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -3390,7 +3390,6 @@ static PyMethodDef math_methods[] = {
     {"asin",            math_asin,      METH_O,         math_asin_doc},
     {"asinh",           math_asinh,     METH_O,         math_asinh_doc},
     {"atan",            math_atan,      METH_O,         math_atan_doc},
-    {"lcm",             math_lcm,       METH_O,         math_lcm_doc},
     {"atan2",           (PyCFunction)(void(*)(void))math_atan2,     METH_FASTCALL,  math_atan2_doc},
     {"atanh",           math_atanh,     METH_O,         math_atanh_doc},
     MATH_CEIL_METHODDEF
@@ -3417,6 +3416,7 @@ static PyMethodDef math_methods[] = {
     MATH_ISINF_METHODDEF
     MATH_ISNAN_METHODDEF
     MATH_ISQRT_METHODDEF
+    MATH_LCM_METHODDEF
     MATH_LDEXP_METHODDEF
     {"lgamma",          math_lgamma,    METH_O,         math_lgamma_doc},
     MATH_LOG_METHODDEF

From 389c49741dc316aa8b8e3a5dff2355745d35d5d4 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Wed, 5 Feb 2020 00:45:53 +0530
Subject: [PATCH 34/83] Update mathmodule.c.h

---
 Modules/clinic/mathmodule.c.h | 32 +++++++++++++++++++++++++++++++-
 1 file changed, 31 insertions(+), 1 deletion(-)

diff --git a/Modules/clinic/mathmodule.c.h b/Modules/clinic/mathmodule.c.h
index f95d291d41f804..df45a1a0c5e855 100644
--- a/Modules/clinic/mathmodule.c.h
+++ b/Modules/clinic/mathmodule.c.h
@@ -85,6 +85,36 @@ PyDoc_STRVAR(math_factorial__doc__,
 #define MATH_FACTORIAL_METHODDEF    \
     {"factorial", (PyCFunction)math_factorial, METH_O, math_factorial__doc__},
 
+PyDoc_STRVAR(math_lcm__doc__,
+"lcm($module, x, y, /)\n"
+"--\n"
+"\n"
+"least common multiple of x and y");
+
+#define MATH_LCM_METHODDEF    \
+    {"lcm", (PyCFunction)(void(*)(void))math_lcm, METH_FASTCALL, math_lcm__doc__},
+
+static PyObject *
+math_lcm_impl(PyObject *module, PyObject *a, PyObject *b);
+
+static PyObject *
+math_lcm(PyObject *module, PyObject *const *args, Py_ssize_t nargs)
+{
+    PyObject *return_value = NULL;
+    PyObject *a;
+    PyObject *b;
+
+    if (!_PyArg_CheckPositional("lcm", nargs, 2, 2)) {
+        goto exit;
+    }
+    a = args[0];
+    b = args[1];
+    return_value = math_lcm_impl(module, a, b);
+
+exit:
+    return return_value;
+}
+
 PyDoc_STRVAR(math_trunc__doc__,
 "trunc($module, x, /)\n"
 "--\n"
@@ -895,4 +925,4 @@ math_ulp(PyObject *module, PyObject *arg)
 exit:
     return return_value;
 }
-/*[clinic end generated code: output=9b51d215dbcac060 input=a9049054013a1b77]*/
+/*[clinic end generated code: output=f8daa185c043a7b7 input=a9049054013a1b77]*/

From 97da5b8aadc56ed84eb4ec825097702270b447c4 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Wed, 5 Feb 2020 00:53:01 +0530
Subject: [PATCH 35/83] Update mathmodule.c

---
 Modules/mathmodule.c | 11 ++++++-----
 1 file changed, 6 insertions(+), 5 deletions(-)

diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index 8cd9d94964c38a..de2f3a1a1daf1b 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -2019,12 +2019,16 @@ math_factorial(PyObject *module, PyObject *arg)
 /*[clinic input]
 math.lcm
 
-	x as a: object
-	y as b: object
+    x as a: object
+    y as b: object
     /
 least common multiple of x and y
 [clinic start generated code]*/
 
+static PyObject *
+math_lcm_impl(PyObject *module, PyObject *a, PyObject *b)
+/*[clinic end generated code: output=6f83fb6d671074ba input=bd41b785dc2a4ff1]*/
+
 static PyObject*
 math_lcm(PyObject *module, PyObject *a, PyObject *b)
 {
@@ -2041,14 +2045,12 @@ math_lcm(PyObject *module, PyObject *a, PyObject *b)
     }
     g = _PyLong_GCD(a, b);
     if (g == NULL) {
-        Py_DECREF(a);
         Py_DECREF(b);
         return NULL;
     }     
     m = PyNumber_Multiply(g, a);
     Py_DECREF(g);
     if (m == NULL) {
-        Py_DECREF(g);
         Py_DECREF(a);
         return NULL;
     }    
@@ -2056,7 +2058,6 @@ math_lcm(PyObject *module, PyObject *a, PyObject *b)
     Py_DECREF(m);
     if (f == NULL) {
         Py_DECREF(a);
-        Py_DECREF(m);
         return NULL;
     }
     ab = PyNumber_Absolute(f);

From bc6490bdc676b3f2f130f6ddc9fbc41a943ca90f Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Wed, 5 Feb 2020 17:43:15 +0530
Subject: [PATCH 36/83] Update mathmodule.c

---
 Modules/mathmodule.c | 1 +
 1 file changed, 1 insertion(+)

diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index de2f3a1a1daf1b..2c347a22e79785 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -2045,6 +2045,7 @@ math_lcm(PyObject *module, PyObject *a, PyObject *b)
     }
     g = _PyLong_GCD(a, b);
     if (g == NULL) {
+        Py_DECREF(a);
         Py_DECREF(b);
         return NULL;
     }     

From 227dee6188a4c7fbe6e917262f68c7fec5837779 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Thu, 6 Feb 2020 17:54:00 +0530
Subject: [PATCH 37/83] Update mathmodule.c

---
 Modules/mathmodule.c | 3 ---
 1 file changed, 3 deletions(-)

diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index 2c347a22e79785..9fce4f285b00c2 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -2028,9 +2028,6 @@ least common multiple of x and y
 static PyObject *
 math_lcm_impl(PyObject *module, PyObject *a, PyObject *b)
 /*[clinic end generated code: output=6f83fb6d671074ba input=bd41b785dc2a4ff1]*/
-
-static PyObject*
-math_lcm(PyObject *module, PyObject *a, PyObject *b)
 {
     PyObject *g, *m, *f, *ab;
 	

From 177d42c5d0a7d83d5c465452ea4276ecfb13bff5 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Fri, 7 Feb 2020 16:17:21 +0530
Subject: [PATCH 38/83] Update Lib/test/test_math.py

Co-Authored-By: Dong-hee Na <donghee.na92@gmail.com>
---
 Lib/test/test_math.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Lib/test/test_math.py b/Lib/test/test_math.py
index 2c6415dbf57c65..24a46f0084d405 100644
--- a/Lib/test/test_math.py
+++ b/Lib/test/test_math.py
@@ -974,7 +974,7 @@ def __index__(self):
                 with self.assertRaises(TypeError):
                     math.isqrt(value)
 
-     def test_lcm(self):
+    def test_lcm(self):
         lcm = math.lcm
         self.assertEqual(lcm(0, 0), 0)
         self.assertEqual(lcm(1, 0), 0)

From e7e5a84bcc5c33fe67d3814ca809112e5da0d9ff Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Fri, 7 Feb 2020 16:17:43 +0530
Subject: [PATCH 39/83] Update Lib/test/test_math.py

Co-Authored-By: Dong-hee Na <donghee.na92@gmail.com>
---
 Lib/test/test_math.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Lib/test/test_math.py b/Lib/test/test_math.py
index 24a46f0084d405..3a46566f9ee404 100644
--- a/Lib/test/test_math.py
+++ b/Lib/test/test_math.py
@@ -993,7 +993,7 @@ def test_lcm(self):
         y = 1064502245825115327754847244914921553977
         
         for c in (652560,
-                  576559230871654959816130551884856912003141446781646602790216406874)
+                  576559230871654959816130551884856912003141446781646602790216406874):
             a = x * c
             b = y * c
             d = x * y * c

From 26ca487aadf6ea667050ad52506fd83f2bd710d3 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Fri, 7 Feb 2020 16:22:35 +0530
Subject: [PATCH 40/83] Update mathmodule.c

---
 Modules/mathmodule.c | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index 9fce4f285b00c2..2ea12ce8646597 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -2046,7 +2046,7 @@ math_lcm_impl(PyObject *module, PyObject *a, PyObject *b)
         Py_DECREF(b);
         return NULL;
     }     
-    m = PyNumber_Multiply(g, a);
+    m = PyNumber_Multiply(g, b);
     Py_DECREF(g);
     if (m == NULL) {
         Py_DECREF(a);

From 30f0226848d6b425c90fe36dc24509cbbcef5f4e Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Fri, 7 Feb 2020 16:31:10 +0530
Subject: [PATCH 41/83] Update mathmodule.c

---
 Modules/mathmodule.c | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index 2ea12ce8646597..ea72bfc6cf263a 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -2059,7 +2059,8 @@ math_lcm_impl(PyObject *module, PyObject *a, PyObject *b)
         return NULL;
     }
     ab = PyNumber_Absolute(f);
-    Py_DECREF(m);
+    Py_DECREF(a);
+    Py_DECREF(b);
     if (ab == NULL) {
         Py_DECREF(f);
         return NULL;

From 08b1fd2586474afe11acf0ca734755aec192f781 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Fri, 7 Feb 2020 16:35:28 +0530
Subject: [PATCH 42/83] Update mathmodule.c

---
 Modules/mathmodule.c | 1 +
 1 file changed, 1 insertion(+)

diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index ea72bfc6cf263a..da27431212bfa8 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -2056,6 +2056,7 @@ math_lcm_impl(PyObject *module, PyObject *a, PyObject *b)
     Py_DECREF(m);
     if (f == NULL) {
         Py_DECREF(a);
+        Py_DECREF(b);
         return NULL;
     }
     ab = PyNumber_Absolute(f);

From d504b862cfd56f291d43b2f8f42dcbdc9b8f6641 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Fri, 7 Feb 2020 16:38:17 +0530
Subject: [PATCH 43/83] Update mathmodule.c

---
 Modules/mathmodule.c | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index da27431212bfa8..106ef357e00884 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -2054,9 +2054,9 @@ math_lcm_impl(PyObject *module, PyObject *a, PyObject *b)
     }    
     f = PyNumber_FloorDivide(a, m);
     Py_DECREF(m);
+    Py_DECREF(b);
     if (f == NULL) {
         Py_DECREF(a);
-        Py_DECREF(b);
         return NULL;
     }
     ab = PyNumber_Absolute(f);

From 53d3af10977c1f10647d7a7a62f8c0b3adb5e4c1 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Fri, 7 Feb 2020 16:40:34 +0530
Subject: [PATCH 44/83] Update mathmodule.c

---
 Modules/mathmodule.c | 1 +
 1 file changed, 1 insertion(+)

diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index 106ef357e00884..5a481aab18fc14 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -2048,6 +2048,7 @@ math_lcm_impl(PyObject *module, PyObject *a, PyObject *b)
     }     
     m = PyNumber_Multiply(g, b);
     Py_DECREF(g);
+    Py_DECREF(b);
     if (m == NULL) {
         Py_DECREF(a);
         return NULL;

From 0700ed6409dd522e4bdad6ae2a1421678b27785a Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Fri, 7 Feb 2020 18:07:27 +0530
Subject: [PATCH 45/83] Update mathmodule.c

---
 Modules/mathmodule.c | 34 ++++++++++++++++++----------------
 1 file changed, 18 insertions(+), 16 deletions(-)

diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index 5a481aab18fc14..9bc39a304c7230 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -2030,43 +2030,45 @@ math_lcm_impl(PyObject *module, PyObject *a, PyObject *b)
 /*[clinic end generated code: output=6f83fb6d671074ba input=bd41b785dc2a4ff1]*/
 {
     PyObject *g, *m, *f, *ab;
-	
+    
     a = PyNumber_Index(a);
-    if (a == NULL) {
+        if (a == NULL) {
         return NULL;
     }
     b = PyNumber_Index(b);
     if (b == NULL) {
-        Py_DECREF(a);
         return NULL;
     }
     g = _PyLong_GCD(a, b);
+    Py_DECREF(a);
+    Py_DECREF(b);
+    Py_DECREF(a);
+    Py_DECREF(b);
     if (g == NULL) {
-        Py_DECREF(a);
-        Py_DECREF(b);
         return NULL;
     }     
-    m = PyNumber_Multiply(g, b);
+    f = PyNumber_FloorDivide(a, g);
+    Py_DECREF(a);
     Py_DECREF(g);
+    Py_DECREF(g);
+    if (f == NULL) {
+        return NULL;
+    }
+    m = PyNumber_Multiply(f, b);
+    Py_DECREF(f);
+    Py_DECREF(f);
     Py_DECREF(b);
     if (m == NULL) {
-        Py_DECREF(a);
         return NULL;
     }    
-    f = PyNumber_FloorDivide(a, m);
+    ab = PyNumber_Absolute(m);
     Py_DECREF(m);
-    Py_DECREF(b);
-    if (f == NULL) {
-        Py_DECREF(a);
+    Py_DECREF(m);
+    if (ab == NULL) {
         return NULL;
     }
-    ab = PyNumber_Absolute(f);
     Py_DECREF(a);
     Py_DECREF(b);
-    if (ab == NULL) {
-        Py_DECREF(f);
-        return NULL;
-    }
     return ab;
 }
 

From e45850791ca9a91faea7c688f9f3e34a9ea51088 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Fri, 7 Feb 2020 20:37:08 +0530
Subject: [PATCH 46/83] Update mathmodule.c

---
 Modules/mathmodule.c | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index 9bc39a304c7230..cc4e75c5925d40 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -2039,6 +2039,9 @@ math_lcm_impl(PyObject *module, PyObject *a, PyObject *b)
     if (b == NULL) {
         return NULL;
     }
+    if(a == 0 || b==0) {
+    return 0;
+    }
     g = _PyLong_GCD(a, b);
     Py_DECREF(a);
     Py_DECREF(b);

From 67aad6160af79837431cea908e66a6af9e6cdbf0 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Fri, 7 Feb 2020 20:48:19 +0530
Subject: [PATCH 47/83] Update math.rst

---
 Doc/library/math.rst | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Doc/library/math.rst b/Doc/library/math.rst
index 88384ff02da2de..59edf1f8dfa9f7 100644
--- a/Doc/library/math.rst
+++ b/Doc/library/math.rst
@@ -139,9 +139,9 @@ Number-theoretic and representation functions
 .. function:: lcm(a, b)
 
    Return the least common multiple of integers *a* and *b*.  If both *a* or
-   *b* is nonzero, then the value of ``lcm(a, b)`` is the smallest positive 
+   *b* is nonzero, then the value of ``lcm(a, b)`` is the smallest positive
    integer that is multiple of both *a* and *b*.  ``lcm(0, 0)`` returns ``0``.
-  
+   
    .. versionadded:: 3.9
 
 

From 517912b462080a122ea8b4f0c19082cfdfdba9fb Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Fri, 7 Feb 2020 20:50:47 +0530
Subject: [PATCH 48/83] Update 3.9.rst

---
 Doc/whatsnew/3.9.rst | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Doc/whatsnew/3.9.rst b/Doc/whatsnew/3.9.rst
index 7700d4cc36e0d8..95d173fa6ea674 100644
--- a/Doc/whatsnew/3.9.rst
+++ b/Doc/whatsnew/3.9.rst
@@ -217,7 +217,7 @@ of a float.
 (Contributed by Victor Stinner in :issue:`39310`.)
 
 Add :func:`math.lcm`: return the least common multiple of *a* and *b*.
-(Contributed by Ananthakrishnan in :issue:`39479`.) 
+(Contributed by Ananthakrishnan in :issue:`39479`.)
 
 nntplib
 -------

From 375c2581f6183a2ce7f1f5a6442cae6d688d5f11 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Fri, 7 Feb 2020 20:56:31 +0530
Subject: [PATCH 49/83] Update math.rst

---
 Doc/library/math.rst | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Doc/library/math.rst b/Doc/library/math.rst
index 59edf1f8dfa9f7..19709fe90e8ff0 100644
--- a/Doc/library/math.rst
+++ b/Doc/library/math.rst
@@ -141,7 +141,7 @@ Number-theoretic and representation functions
    Return the least common multiple of integers *a* and *b*.  If both *a* or
    *b* is nonzero, then the value of ``lcm(a, b)`` is the smallest positive
    integer that is multiple of both *a* and *b*.  ``lcm(0, 0)`` returns ``0``.
-   
+
    .. versionadded:: 3.9
 
 

From 76fed5d5f8d056334c572247828a22b4a56184da Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Fri, 7 Feb 2020 21:06:39 +0530
Subject: [PATCH 50/83] Update mathmodule.c

---
 Modules/mathmodule.c | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index cc4e75c5925d40..5205ab4fbd019b 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -2042,6 +2042,7 @@ math_lcm_impl(PyObject *module, PyObject *a, PyObject *b)
     if(a == 0 || b==0) {
     return 0;
     }
+    else {
     g = _PyLong_GCD(a, b);
     Py_DECREF(a);
     Py_DECREF(b);
@@ -2073,6 +2074,7 @@ math_lcm_impl(PyObject *module, PyObject *a, PyObject *b)
     Py_DECREF(a);
     Py_DECREF(b);
     return ab;
+    }
 }
 
 

From d128e2d96b327239394eb3272603bcfa698e294a Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Fri, 7 Feb 2020 21:15:52 +0530
Subject: [PATCH 51/83] Update test_math.py

---
 Lib/test/test_math.py | 5 ++---
 1 file changed, 2 insertions(+), 3 deletions(-)

diff --git a/Lib/test/test_math.py b/Lib/test/test_math.py
index 3a46566f9ee404..653f08b157cd37 100644
--- a/Lib/test/test_math.py
+++ b/Lib/test/test_math.py
@@ -991,7 +991,6 @@ def test_lcm(self):
                              16592536571065866494401400422922201534178938447014944)
         x = 434610456570399902378880679233098819019853229470286994367836600566
         y = 1064502245825115327754847244914921553977
-        
         for c in (652560,
                   576559230871654959816130551884856912003141446781646602790216406874):
             a = x * c
@@ -1004,10 +1003,10 @@ def test_lcm(self):
             self.assertEqual(lcm(a, -b), d)
             self.assertEqual(lcm(-b, a), d)
             self.assertEqual(lcm(-a, -b), d)
-            self.assertEqual(lcm(-b, -a), d)    
+            self.assertEqual(lcm(-b, -a), d)
         self.assertRaises(TypeError, lcm, 120.0, 84)
         self.assertRaises(TypeError, lcm, 120, 84.0)
-        
+
     def testLdexp(self):
         self.assertRaises(TypeError, math.ldexp)
         self.ftest('ldexp(0,1)', math.ldexp(0,1), 0)

From e009376c947c2cd1ba66bbe0e2de0ee93e67d02c Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Fri, 7 Feb 2020 21:30:35 +0530
Subject: [PATCH 52/83] Update test_math.py

---
 Lib/test/test_math.py | 1 -
 1 file changed, 1 deletion(-)

diff --git a/Lib/test/test_math.py b/Lib/test/test_math.py
index 653f08b157cd37..47e3c75d53e466 100644
--- a/Lib/test/test_math.py
+++ b/Lib/test/test_math.py
@@ -976,7 +976,6 @@ def __index__(self):
 
     def test_lcm(self):
         lcm = math.lcm
-        self.assertEqual(lcm(0, 0), 0)
         self.assertEqual(lcm(1, 0), 0)
         self.assertEqual(lcm(-1, 0), 0)
         self.assertEqual(lcm(0, 1), 0)

From 4a4f24171fe146fcd637327b9fcc6817d9199194 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Fri, 7 Feb 2020 21:32:31 +0530
Subject: [PATCH 53/83] Update mathmodule.c

---
 Modules/mathmodule.c | 5 -----
 1 file changed, 5 deletions(-)

diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index 5205ab4fbd019b..9bc39a304c7230 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -2039,10 +2039,6 @@ math_lcm_impl(PyObject *module, PyObject *a, PyObject *b)
     if (b == NULL) {
         return NULL;
     }
-    if(a == 0 || b==0) {
-    return 0;
-    }
-    else {
     g = _PyLong_GCD(a, b);
     Py_DECREF(a);
     Py_DECREF(b);
@@ -2074,7 +2070,6 @@ math_lcm_impl(PyObject *module, PyObject *a, PyObject *b)
     Py_DECREF(a);
     Py_DECREF(b);
     return ab;
-    }
 }
 
 

From a596a839d9ae8bec1208e38b754efa643288957a Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Fri, 7 Feb 2020 22:18:12 +0530
Subject: [PATCH 54/83] Update mathmodule.c

---
 Modules/mathmodule.c | 15 ++++++++++++++-
 1 file changed, 14 insertions(+), 1 deletion(-)

diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index 9bc39a304c7230..21f97d776ef855 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -2039,6 +2039,14 @@ math_lcm_impl(PyObject *module, PyObject *a, PyObject *b)
     if (b == NULL) {
         return NULL;
     }
+    if (PyString_Check(a) || PyString_Check(b)) {
+        PyErr_Format(PyExc_TypeError,"'str' object cannot be an argument to lcm");
+        return;  
+    }
+    if (PyFloat_Check(a) || PyFloat_Check(b)) {
+        PyErr_Format(PyExc_TypeError,"'float' object cannot be an argument to lcm");
+        return;  
+    }
     g = _PyLong_GCD(a, b);
     Py_DECREF(a);
     Py_DECREF(b);
@@ -2046,11 +2054,16 @@ math_lcm_impl(PyObject *module, PyObject *a, PyObject *b)
     Py_DECREF(b);
     if (g == NULL) {
         return NULL;
-    }     
+    }
+    if (g==0) {
+        f=0;
+    }
+    else {
     f = PyNumber_FloorDivide(a, g);
     Py_DECREF(a);
     Py_DECREF(g);
     Py_DECREF(g);
+    }
     if (f == NULL) {
         return NULL;
     }

From 92cd405278a7c2946d0241bb846823822eb81d14 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Fri, 7 Feb 2020 22:21:51 +0530
Subject: [PATCH 55/83] Update test_math.py

---
 Lib/test/test_math.py | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/Lib/test/test_math.py b/Lib/test/test_math.py
index 47e3c75d53e466..c8f476c58232a4 100644
--- a/Lib/test/test_math.py
+++ b/Lib/test/test_math.py
@@ -976,6 +976,7 @@ def __index__(self):
 
     def test_lcm(self):
         lcm = math.lcm
+        self.assertEqual(lcm(0, 0), 0)
         self.assertEqual(lcm(1, 0), 0)
         self.assertEqual(lcm(-1, 0), 0)
         self.assertEqual(lcm(0, 1), 0)
@@ -990,6 +991,7 @@ def test_lcm(self):
                              16592536571065866494401400422922201534178938447014944)
         x = 434610456570399902378880679233098819019853229470286994367836600566
         y = 1064502245825115327754847244914921553977
+
         for c in (652560,
                   576559230871654959816130551884856912003141446781646602790216406874):
             a = x * c
@@ -1005,6 +1007,9 @@ def test_lcm(self):
             self.assertEqual(lcm(-b, -a), d)
         self.assertRaises(TypeError, lcm, 120.0, 84)
         self.assertRaises(TypeError, lcm, 120, 84.0)
+        self.assertRaises(TypeError, lcm, "a", 7)
+        self.assertRaises(TypeError, lcm, 7, "a")
+        self.assertRaises(TypeError, lcm, "a", "a")
 
     def testLdexp(self):
         self.assertRaises(TypeError, math.ldexp)

From c069214b0097a644d5b7ea6153a75996928c9460 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Fri, 7 Feb 2020 22:28:13 +0530
Subject: [PATCH 56/83] Update mathmodule.c

---
 Modules/mathmodule.c | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index 21f97d776ef855..0c52918e99aa6f 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -2039,13 +2039,13 @@ math_lcm_impl(PyObject *module, PyObject *a, PyObject *b)
     if (b == NULL) {
         return NULL;
     }
-    if (PyString_Check(a) || PyString_Check(b)) {
+    if (PyStr_Check(a) || PyStr_Check(b)) {
         PyErr_Format(PyExc_TypeError,"'str' object cannot be an argument to lcm");
-        return;  
+        return 0;  
     }
     if (PyFloat_Check(a) || PyFloat_Check(b)) {
         PyErr_Format(PyExc_TypeError,"'float' object cannot be an argument to lcm");
-        return;  
+        return 0;  
     }
     g = _PyLong_GCD(a, b);
     Py_DECREF(a);

From 8543b035ada645cfb39837bbdff044e040833cf8 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Fri, 7 Feb 2020 22:46:47 +0530
Subject: [PATCH 57/83] Update mathmodule.c

---
 Modules/mathmodule.c | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index 0c52918e99aa6f..734be809374f5d 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -2039,7 +2039,7 @@ math_lcm_impl(PyObject *module, PyObject *a, PyObject *b)
     if (b == NULL) {
         return NULL;
     }
-    if (PyStr_Check(a) || PyStr_Check(b)) {
+    if (PyObject_TypeCheck(a, PyBytes_Type) || PyObject_TypeCheck(b, PyBytes_Type)) {
         PyErr_Format(PyExc_TypeError,"'str' object cannot be an argument to lcm");
         return 0;  
     }

From 4566c08a1a14957b52d321b39cffae761babacec Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Fri, 7 Feb 2020 22:53:55 +0530
Subject: [PATCH 58/83] Update mathmodule.c

---
 Modules/mathmodule.c | 4 ----
 1 file changed, 4 deletions(-)

diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index 734be809374f5d..086c3f5943a1d7 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -2039,10 +2039,6 @@ math_lcm_impl(PyObject *module, PyObject *a, PyObject *b)
     if (b == NULL) {
         return NULL;
     }
-    if (PyObject_TypeCheck(a, PyBytes_Type) || PyObject_TypeCheck(b, PyBytes_Type)) {
-        PyErr_Format(PyExc_TypeError,"'str' object cannot be an argument to lcm");
-        return 0;  
-    }
     if (PyFloat_Check(a) || PyFloat_Check(b)) {
         PyErr_Format(PyExc_TypeError,"'float' object cannot be an argument to lcm");
         return 0;  

From 66e6d6536c6f0de19b3b673bd742f915e0669c1e Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Fri, 7 Feb 2020 23:05:58 +0530
Subject: [PATCH 59/83] Update mathmodule.c

---
 Modules/mathmodule.c | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index 086c3f5943a1d7..65f101959fb299 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -2051,8 +2051,8 @@ math_lcm_impl(PyObject *module, PyObject *a, PyObject *b)
     if (g == NULL) {
         return NULL;
     }
-    if (g==0) {
-        f=0;
+    if (g == 0) {
+        f = 0;
     }
     else {
     f = PyNumber_FloorDivide(a, g);

From c063ea31d0834e1c1e4cff774a22e1e114af9806 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Fri, 7 Feb 2020 23:07:00 +0530
Subject: [PATCH 60/83] Update test_math.py

---
 Lib/test/test_math.py | 3 ---
 1 file changed, 3 deletions(-)

diff --git a/Lib/test/test_math.py b/Lib/test/test_math.py
index c8f476c58232a4..46dd58be28091a 100644
--- a/Lib/test/test_math.py
+++ b/Lib/test/test_math.py
@@ -1007,9 +1007,6 @@ def test_lcm(self):
             self.assertEqual(lcm(-b, -a), d)
         self.assertRaises(TypeError, lcm, 120.0, 84)
         self.assertRaises(TypeError, lcm, 120, 84.0)
-        self.assertRaises(TypeError, lcm, "a", 7)
-        self.assertRaises(TypeError, lcm, 7, "a")
-        self.assertRaises(TypeError, lcm, "a", "a")
 
     def testLdexp(self):
         self.assertRaises(TypeError, math.ldexp)

From f45794846f8ea9f6a4e4962a8bb540c94ec8c6a4 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Fri, 7 Feb 2020 23:16:07 +0530
Subject: [PATCH 61/83] Update test_math.py

---
 Lib/test/test_math.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Lib/test/test_math.py b/Lib/test/test_math.py
index 46dd58be28091a..849fcd08304785 100644
--- a/Lib/test/test_math.py
+++ b/Lib/test/test_math.py
@@ -976,7 +976,6 @@ def __index__(self):
 
     def test_lcm(self):
         lcm = math.lcm
-        self.assertEqual(lcm(0, 0), 0)
         self.assertEqual(lcm(1, 0), 0)
         self.assertEqual(lcm(-1, 0), 0)
         self.assertEqual(lcm(0, 1), 0)
@@ -1007,6 +1006,7 @@ def test_lcm(self):
             self.assertEqual(lcm(-b, -a), d)
         self.assertRaises(TypeError, lcm, 120.0, 84)
         self.assertRaises(TypeError, lcm, 120, 84.0)
+        self.assertRaises(ZeroDivisionError, lcm, 0, 0)
 
     def testLdexp(self):
         self.assertRaises(TypeError, math.ldexp)

From ea7273509de84937a10d6f7e76c3e87798cf5288 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Fri, 7 Feb 2020 23:21:25 +0530
Subject: [PATCH 62/83] Update mathmodule.c

---
 Modules/mathmodule.c | 9 ++++-----
 1 file changed, 4 insertions(+), 5 deletions(-)

diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index 65f101959fb299..256e41d8967180 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -2039,6 +2039,10 @@ math_lcm_impl(PyObject *module, PyObject *a, PyObject *b)
     if (b == NULL) {
         return NULL;
     }
+    if (a == 0 && b == 0) {
+       PyErr_Format(PyExc_ZeroDivisionError,"lcm(0,0) is not possible");
+       return 0;
+    }
     if (PyFloat_Check(a) || PyFloat_Check(b)) {
         PyErr_Format(PyExc_TypeError,"'float' object cannot be an argument to lcm");
         return 0;  
@@ -2051,15 +2055,10 @@ math_lcm_impl(PyObject *module, PyObject *a, PyObject *b)
     if (g == NULL) {
         return NULL;
     }
-    if (g == 0) {
-        f = 0;
-    }
-    else {
     f = PyNumber_FloorDivide(a, g);
     Py_DECREF(a);
     Py_DECREF(g);
     Py_DECREF(g);
-    }
     if (f == NULL) {
         return NULL;
     }

From 46f10f2e506c3ebb64192eacc8a900dbb4ffad73 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Fri, 7 Feb 2020 23:34:36 +0530
Subject: [PATCH 63/83] Update mathmodule.c

---
 Modules/mathmodule.c | 1 -
 1 file changed, 1 deletion(-)

diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index 256e41d8967180..cdc600a2774d77 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -2071,7 +2071,6 @@ math_lcm_impl(PyObject *module, PyObject *a, PyObject *b)
     }    
     ab = PyNumber_Absolute(m);
     Py_DECREF(m);
-    Py_DECREF(m);
     if (ab == NULL) {
         return NULL;
     }

From 5b4428b5b67c5410e600a2274085fe64268f84d3 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Fri, 7 Feb 2020 23:47:48 +0530
Subject: [PATCH 64/83] Update mathmodule.c

---
 Modules/mathmodule.c | 1 -
 1 file changed, 1 deletion(-)

diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index cdc600a2774d77..30de9f250f113e 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -2064,7 +2064,6 @@ math_lcm_impl(PyObject *module, PyObject *a, PyObject *b)
     }
     m = PyNumber_Multiply(f, b);
     Py_DECREF(f);
-    Py_DECREF(f);
     Py_DECREF(b);
     if (m == NULL) {
         return NULL;

From 6caf90085972a5f003d99bfa87dfa7b1425503c5 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Sat, 8 Feb 2020 21:11:20 +0530
Subject: [PATCH 65/83] Update mathmodule.c

---
 Modules/mathmodule.c | 72 ++++++++++++++++++++++----------------------
 1 file changed, 36 insertions(+), 36 deletions(-)

diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index 30de9f250f113e..6259bf7e2efd71 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -2033,49 +2033,49 @@ math_lcm_impl(PyObject *module, PyObject *a, PyObject *b)
     
     a = PyNumber_Index(a);
         if (a == NULL) {
-        return NULL;
+            return NULL;
     }
     b = PyNumber_Index(b);
     if (b == NULL) {
         return NULL;
     }
-    if (a == 0 && b == 0) {
-       PyErr_Format(PyExc_ZeroDivisionError,"lcm(0,0) is not possible");
-       return 0;
-    }
-    if (PyFloat_Check(a) || PyFloat_Check(b)) {
-        PyErr_Format(PyExc_TypeError,"'float' object cannot be an argument to lcm");
-        return 0;  
-    }
-    g = _PyLong_GCD(a, b);
-    Py_DECREF(a);
-    Py_DECREF(b);
-    Py_DECREF(a);
-    Py_DECREF(b);
-    if (g == NULL) {
-        return NULL;
-    }
-    f = PyNumber_FloorDivide(a, g);
-    Py_DECREF(a);
-    Py_DECREF(g);
-    Py_DECREF(g);
-    if (f == NULL) {
-        return NULL;
+    if (a == 0) {
+        return 0;
     }
-    m = PyNumber_Multiply(f, b);
-    Py_DECREF(f);
-    Py_DECREF(b);
-    if (m == NULL) {
-        return NULL;
-    }    
-    ab = PyNumber_Absolute(m);
-    Py_DECREF(m);
-    if (ab == NULL) {
-        return NULL;
+    else {
+        if (PyFloat_Check(a) || PyFloat_Check(b)) {
+            PyErr_Format(PyExc_TypeError,"'float' object cannot be an argument to lcm");
+            return 0;  
+        }
+        g = _PyLong_GCD(a, b);
+        Py_DECREF(a);
+        Py_DECREF(b);
+        Py_DECREF(b);
+        if (g == NULL) {
+            return NULL;
+        }
+        f = PyNumber_FloorDivide(a, g);
+        Py_DECREF(a);
+        Py_DECREF(g);
+        Py_DECREF(g);
+        if (f == NULL) {
+            return NULL;
+        }
+        m = PyNumber_Multiply(f, b);
+        Py_DECREF(f);
+        Py_DECREF(b);
+        if (m == NULL) {
+            return NULL;
+        }    
+        ab = PyNumber_Absolute(m);
+        Py_DECREF(m);
+        if (ab == NULL) {
+            return NULL;
+        }
+        Py_DECREF(a);
+        Py_DECREF(b);
+        return ab;
     }
-    Py_DECREF(a);
-    Py_DECREF(b);
-    return ab;
 }
 
 

From 911570be63a83dcf9eca231d9e37fbfd79e03e90 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Sat, 8 Feb 2020 21:12:13 +0530
Subject: [PATCH 66/83] Update test_math.py

---
 Lib/test/test_math.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Lib/test/test_math.py b/Lib/test/test_math.py
index 849fcd08304785..46dd58be28091a 100644
--- a/Lib/test/test_math.py
+++ b/Lib/test/test_math.py
@@ -976,6 +976,7 @@ def __index__(self):
 
     def test_lcm(self):
         lcm = math.lcm
+        self.assertEqual(lcm(0, 0), 0)
         self.assertEqual(lcm(1, 0), 0)
         self.assertEqual(lcm(-1, 0), 0)
         self.assertEqual(lcm(0, 1), 0)
@@ -1006,7 +1007,6 @@ def test_lcm(self):
             self.assertEqual(lcm(-b, -a), d)
         self.assertRaises(TypeError, lcm, 120.0, 84)
         self.assertRaises(TypeError, lcm, 120, 84.0)
-        self.assertRaises(ZeroDivisionError, lcm, 0, 0)
 
     def testLdexp(self):
         self.assertRaises(TypeError, math.ldexp)

From 24ba4c8d2d53364a9b633b669e4d07685a5496a0 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Sat, 8 Feb 2020 21:22:19 +0530
Subject: [PATCH 67/83] Update mathmodule.c

---
 Modules/mathmodule.c | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index 6259bf7e2efd71..6c31e6e947f33e 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -2039,7 +2039,7 @@ math_lcm_impl(PyObject *module, PyObject *a, PyObject *b)
     if (b == NULL) {
         return NULL;
     }
-    if (a == 0) {
+    if (a == 0 && b == 0) {
         return 0;
     }
     else {

From b097bc6d20fb138e7d29264339bbd60c37f9a66b Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Sat, 8 Feb 2020 21:30:24 +0530
Subject: [PATCH 68/83] Update test_math.py

---
 Lib/test/test_math.py | 1 -
 1 file changed, 1 deletion(-)

diff --git a/Lib/test/test_math.py b/Lib/test/test_math.py
index 46dd58be28091a..e532fa346871cd 100644
--- a/Lib/test/test_math.py
+++ b/Lib/test/test_math.py
@@ -976,7 +976,6 @@ def __index__(self):
 
     def test_lcm(self):
         lcm = math.lcm
-        self.assertEqual(lcm(0, 0), 0)
         self.assertEqual(lcm(1, 0), 0)
         self.assertEqual(lcm(-1, 0), 0)
         self.assertEqual(lcm(0, 1), 0)

From ddf5a39c442ff12a522d53cd1a9432f77299fdec Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Sat, 15 Feb 2020 18:11:49 +0530
Subject: [PATCH 69/83] Update mathmodule.c

---
 Modules/mathmodule.c | 58 +++++++++++++++++++-------------------------
 1 file changed, 25 insertions(+), 33 deletions(-)

diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index 6c31e6e947f33e..7fce1675526fa5 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -2032,55 +2032,47 @@ math_lcm_impl(PyObject *module, PyObject *a, PyObject *b)
     PyObject *g, *m, *f, *ab;
     
     a = PyNumber_Index(a);
-        if (a == NULL) {
-            return NULL;
+    if (a == NULL) {
+        return NULL;
     }
     b = PyNumber_Index(b);
     if (b == NULL) {
+        Py_DECREF(a);
         return NULL;
     }
-    if (a == 0 && b == 0) {
-        return 0;
-    }
-    else {
-        if (PyFloat_Check(a) || PyFloat_Check(b)) {
-            PyErr_Format(PyExc_TypeError,"'float' object cannot be an argument to lcm");
-            return 0;  
-        }
-        g = _PyLong_GCD(a, b);
+    g = _PyLong_GCD(a, b);
+    if (g == NULL) {
         Py_DECREF(a);
         Py_DECREF(b);
+        return NULL;
+    }
+    f = PyNumber_FloorDivide(a, g);
+    Py_DECREF(g);
+    if (f == NULL) {
+        Py_DECREF(a);
         Py_DECREF(b);
-        if (g == NULL) {
-            return NULL;
-        }
-        f = PyNumber_FloorDivide(a, g);
+        return NULL;
+    }
+    m = PyNumber_Multiply(f, b);
+    Py_DECREF(f);
+    if (m == NULL) {
         Py_DECREF(a);
-        Py_DECREF(g);
-        Py_DECREF(g);
-        if (f == NULL) {
-            return NULL;
-        }
-        m = PyNumber_Multiply(f, b);
-        Py_DECREF(f);
         Py_DECREF(b);
-        if (m == NULL) {
-            return NULL;
-        }    
-        ab = PyNumber_Absolute(m);
-        Py_DECREF(m);
-        if (ab == NULL) {
-            return NULL;
-        }
+        return NULL;
+    }    
+    ab = PyNumber_Absolute(m);
+    Py_DECREF(m);
+    if (ab == NULL) {
         Py_DECREF(a);
         Py_DECREF(b);
-        return ab;
+        return NULL;
     }
+    Py_DECREF(a);
+    Py_DECREF(b);
+    return ab;
 }
 
 
-
-
 /*[clinic input]
 math.trunc
 

From 37f52331848c616edcc5ad7b1bf669ef588f6ecc Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Sat, 15 Feb 2020 18:26:50 +0530
Subject: [PATCH 70/83] Update mathmodule.c

---
 Modules/mathmodule.c | 9 ++-------
 1 file changed, 2 insertions(+), 7 deletions(-)

diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index 7fce1675526fa5..41199464b1847b 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -2048,27 +2048,22 @@ math_lcm_impl(PyObject *module, PyObject *a, PyObject *b)
     }
     f = PyNumber_FloorDivide(a, g);
     Py_DECREF(g);
+    Py_DECREF(a);
     if (f == NULL) {
-        Py_DECREF(a);
         Py_DECREF(b);
         return NULL;
     }
     m = PyNumber_Multiply(f, b);
     Py_DECREF(f);
+    Py_DECREF(b);
     if (m == NULL) {
-        Py_DECREF(a);
-        Py_DECREF(b);
         return NULL;
     }    
     ab = PyNumber_Absolute(m);
     Py_DECREF(m);
     if (ab == NULL) {
-        Py_DECREF(a);
-        Py_DECREF(b);
         return NULL;
     }
-    Py_DECREF(a);
-    Py_DECREF(b);
     return ab;
 }
 

From 3074e34fcb5f8524046c3e6e67b3a3b267127e82 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Sat, 15 Feb 2020 18:34:08 +0530
Subject: [PATCH 71/83] Update test_math.py

---
 Lib/test/test_math.py | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/Lib/test/test_math.py b/Lib/test/test_math.py
index e532fa346871cd..02d17bff1a9de4 100644
--- a/Lib/test/test_math.py
+++ b/Lib/test/test_math.py
@@ -976,6 +976,7 @@ def __index__(self):
 
     def test_lcm(self):
         lcm = math.lcm
+        self.assertEqual(lcm(0, 0), 0)
         self.assertEqual(lcm(1, 0), 0)
         self.assertEqual(lcm(-1, 0), 0)
         self.assertEqual(lcm(0, 1), 0)
@@ -1004,8 +1005,6 @@ def test_lcm(self):
             self.assertEqual(lcm(-b, a), d)
             self.assertEqual(lcm(-a, -b), d)
             self.assertEqual(lcm(-b, -a), d)
-        self.assertRaises(TypeError, lcm, 120.0, 84)
-        self.assertRaises(TypeError, lcm, 120, 84.0)
 
     def testLdexp(self):
         self.assertRaises(TypeError, math.ldexp)

From 3bb50dcaf95d10891a75329e93c498ef4ca8ac55 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Sat, 15 Feb 2020 18:55:40 +0530
Subject: [PATCH 72/83] Update mathmodule.c

---
 Modules/mathmodule.c | 3 ---
 1 file changed, 3 deletions(-)

diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index 41199464b1847b..f8cdb6d1cccf29 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -2061,9 +2061,6 @@ math_lcm_impl(PyObject *module, PyObject *a, PyObject *b)
     }    
     ab = PyNumber_Absolute(m);
     Py_DECREF(m);
-    if (ab == NULL) {
-        return NULL;
-    }
     return ab;
 }
 

From e40c94cae8d1bbb9dada32c9033e39a9e2356997 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Sat, 15 Feb 2020 19:26:50 +0530
Subject: [PATCH 73/83] Update mathmodule.c

---
 Modules/mathmodule.c | 43 ++++++++++++++++++++++++-------------------
 1 file changed, 24 insertions(+), 19 deletions(-)

diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index f8cdb6d1cccf29..ee23defab49d53 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -2040,28 +2040,33 @@ math_lcm_impl(PyObject *module, PyObject *a, PyObject *b)
         Py_DECREF(a);
         return NULL;
     }
-    g = _PyLong_GCD(a, b);
-    if (g == NULL) {
-        Py_DECREF(a);
-        Py_DECREF(b);
-        return NULL;
+    if (_PyLong_Sign(a) == 0 && _PyLong_Sign(b) == 0) {
+        return 0;
     }
-    f = PyNumber_FloorDivide(a, g);
-    Py_DECREF(g);
-    Py_DECREF(a);
-    if (f == NULL) {
+    else {
+        g = _PyLong_GCD(a, b);
+        if (g == NULL) {
+            Py_DECREF(a);
+            Py_DECREF(b);
+            return NULL;
+        }
+        f = PyNumber_FloorDivide(a, g);
+        Py_DECREF(g);
+        Py_DECREF(a);
+        if (f == NULL) {
+            Py_DECREF(b);
+            return NULL;
+        }
+        m = PyNumber_Multiply(f, b);
+        Py_DECREF(f);
         Py_DECREF(b);
-        return NULL;
+        if (m == NULL) {
+            return NULL;
+        }    
+        ab = PyNumber_Absolute(m);
+        Py_DECREF(m);
+        return ab;
     }
-    m = PyNumber_Multiply(f, b);
-    Py_DECREF(f);
-    Py_DECREF(b);
-    if (m == NULL) {
-        return NULL;
-    }    
-    ab = PyNumber_Absolute(m);
-    Py_DECREF(m);
-    return ab;
 }
 
 

From 2e95203affa8002653e7e5a7923b4ed1ec130629 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Sat, 15 Feb 2020 21:49:21 +0530
Subject: [PATCH 74/83] Update mathmodule.c

---
 Modules/mathmodule.c | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index ee23defab49d53..a4e8c5aa9ce3c7 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -2041,7 +2041,7 @@ math_lcm_impl(PyObject *module, PyObject *a, PyObject *b)
         return NULL;
     }
     if (_PyLong_Sign(a) == 0 && _PyLong_Sign(b) == 0) {
-        return 0;
+        return PyLong_FromLong(0);
     }
     else {
         g = _PyLong_GCD(a, b);

From afdecfa4fd00d56334baa8661dc3105414d40b27 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Sat, 15 Feb 2020 22:03:35 +0530
Subject: [PATCH 75/83] Update mathmodule.c

---
 Modules/mathmodule.c | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index a4e8c5aa9ce3c7..1741852328211f 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -2041,6 +2041,8 @@ math_lcm_impl(PyObject *module, PyObject *a, PyObject *b)
         return NULL;
     }
     if (_PyLong_Sign(a) == 0 && _PyLong_Sign(b) == 0) {
+        Py_DECREF(a);
+        Py_DECREF(b);
         return PyLong_FromLong(0);
     }
     else {

From aa118d9adafbca30eb5df73f65e27a601075ee2e Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Sat, 15 Feb 2020 22:17:32 +0530
Subject: [PATCH 76/83] changed '&&' to '||'

---
 Modules/mathmodule.c | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index 1741852328211f..a0760119f3bf4b 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -2040,7 +2040,7 @@ math_lcm_impl(PyObject *module, PyObject *a, PyObject *b)
         Py_DECREF(a);
         return NULL;
     }
-    if (_PyLong_Sign(a) == 0 && _PyLong_Sign(b) == 0) {
+    if (_PyLong_Sign(a) == 0 || _PyLong_Sign(b) == 0) {
         Py_DECREF(a);
         Py_DECREF(b);
         return PyLong_FromLong(0);

From 0c03453445d4cbb77cf9fd5624431c074cd73acb Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Sat, 15 Feb 2020 22:41:50 +0530
Subject: [PATCH 77/83] changed gramatical errors

---
 Doc/library/math.rst | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/Doc/library/math.rst b/Doc/library/math.rst
index 19709fe90e8ff0..f3935a68cf4905 100644
--- a/Doc/library/math.rst
+++ b/Doc/library/math.rst
@@ -138,9 +138,9 @@ Number-theoretic and representation functions
 
 .. function:: lcm(a, b)
 
-   Return the least common multiple of integers *a* and *b*.  If both *a* or
-   *b* is nonzero, then the value of ``lcm(a, b)`` is the smallest positive
-   integer that is multiple of both *a* and *b*.  ``lcm(0, 0)`` returns ``0``.
+   Return the least common multiple of integers *a* and *b*.  The value of
+   ``lcm(a, b)`` is the smallest non negative integer that is a multiple of
+   both *a* and *b*.  If either *a* or *b* is zero then ``lcm(a, b)`` is zero.
 
    .. versionadded:: 3.9
 

From 73fe2afd56f8fb240a085cea217bfdbbbb2b8d24 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Sat, 15 Feb 2020 22:51:21 +0530
Subject: [PATCH 78/83] Update math.rst

---
 Doc/library/math.rst | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Doc/library/math.rst b/Doc/library/math.rst
index f3935a68cf4905..d8ac35256d1b4b 100644
--- a/Doc/library/math.rst
+++ b/Doc/library/math.rst
@@ -139,7 +139,7 @@ Number-theoretic and representation functions
 .. function:: lcm(a, b)
 
    Return the least common multiple of integers *a* and *b*.  The value of
-   ``lcm(a, b)`` is the smallest non negative integer that is a multiple of
+   ``lcm(a, b)`` is the smallest nonnegative integer that is a multiple of
    both *a* and *b*.  If either *a* or *b* is zero then ``lcm(a, b)`` is zero.
 
    .. versionadded:: 3.9

From 20e696ff4e61c2809b55941737da8a0172cc8b6e Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Sat, 15 Feb 2020 23:03:52 +0530
Subject: [PATCH 79/83] removed "else" statement.

---
 Modules/mathmodule.c | 40 +++++++++++++++++++---------------------
 1 file changed, 19 insertions(+), 21 deletions(-)

diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index a0760119f3bf4b..3bd53a00a25922 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -2045,30 +2045,28 @@ math_lcm_impl(PyObject *module, PyObject *a, PyObject *b)
         Py_DECREF(b);
         return PyLong_FromLong(0);
     }
-    else {
-        g = _PyLong_GCD(a, b);
-        if (g == NULL) {
-            Py_DECREF(a);
-            Py_DECREF(b);
-            return NULL;
-        }
-        f = PyNumber_FloorDivide(a, g);
-        Py_DECREF(g);
+    g = _PyLong_GCD(a, b);
+    if (g == NULL) {
         Py_DECREF(a);
-        if (f == NULL) {
-            Py_DECREF(b);
-            return NULL;
-        }
-        m = PyNumber_Multiply(f, b);
-        Py_DECREF(f);
         Py_DECREF(b);
-        if (m == NULL) {
-            return NULL;
-        }    
-        ab = PyNumber_Absolute(m);
-        Py_DECREF(m);
-        return ab;
+        return NULL;
     }
+    f = PyNumber_FloorDivide(a, g);
+    Py_DECREF(g);
+    Py_DECREF(a);
+    if (f == NULL) {
+        Py_DECREF(b);
+        return NULL;
+    }
+    m = PyNumber_Multiply(f, b);
+    Py_DECREF(f);
+    Py_DECREF(b);
+    if (m == NULL) {
+        return NULL;
+    }    
+    ab = PyNumber_Absolute(m);
+    Py_DECREF(m);
+    return ab;
 }
 
 

From 54d1be4c40ff6032e5535526ffb94d24dada5b0f Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Sat, 15 Feb 2020 23:36:55 +0530
Subject: [PATCH 80/83] Update
 Misc/NEWS.d/next/Library/2020-02-04-13-47-16.bpo-39479.BN_mM9.rst

Co-Authored-By: Serhiy Storchaka <storchaka@gmail.com>
---
 .../next/Library/2020-02-04-13-47-16.bpo-39479.BN_mM9.rst       | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Misc/NEWS.d/next/Library/2020-02-04-13-47-16.bpo-39479.BN_mM9.rst b/Misc/NEWS.d/next/Library/2020-02-04-13-47-16.bpo-39479.BN_mM9.rst
index cf888d71417f0a..7298ecec4a5201 100644
--- a/Misc/NEWS.d/next/Library/2020-02-04-13-47-16.bpo-39479.BN_mM9.rst
+++ b/Misc/NEWS.d/next/Library/2020-02-04-13-47-16.bpo-39479.BN_mM9.rst
@@ -1 +1 @@
-Add `math.lcm()` function: Least Common Multiple.
\ No newline at end of file
+Add func:`math.lcm` function: Least Common Multiple.

From f4ec2512f3cfc447f87d9d4b40b522ed53757165 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Sat, 15 Feb 2020 23:52:27 +0530
Subject: [PATCH 81/83] Update test_math.py

---
 Lib/test/test_math.py | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/Lib/test/test_math.py b/Lib/test/test_math.py
index 02d17bff1a9de4..58f58a924ca99d 100644
--- a/Lib/test/test_math.py
+++ b/Lib/test/test_math.py
@@ -1005,6 +1005,9 @@ def test_lcm(self):
             self.assertEqual(lcm(-b, a), d)
             self.assertEqual(lcm(-a, -b), d)
             self.assertEqual(lcm(-b, -a), d)
+        self.assertEqual(lcm(MyIndexable(120), MyIndexable(84)), 840)
+        self.assertRaises(TypeError, lcm, 120.0, 84)
+        self.assertRaises(TypeError, lcm, 120, 84.0)
 
     def testLdexp(self):
         self.assertRaises(TypeError, math.ldexp)

From 134c4f4c358b416826e630165a8936e705606edc Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Sun, 16 Feb 2020 23:14:18 +0530
Subject: [PATCH 82/83] Update math.rst

---
 Doc/library/math.rst | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Doc/library/math.rst b/Doc/library/math.rst
index d8ac35256d1b4b..af00b2adb10174 100644
--- a/Doc/library/math.rst
+++ b/Doc/library/math.rst
@@ -140,7 +140,7 @@ Number-theoretic and representation functions
 
    Return the least common multiple of integers *a* and *b*.  The value of
    ``lcm(a, b)`` is the smallest nonnegative integer that is a multiple of
-   both *a* and *b*.  If either *a* or *b* is zero then ``lcm(a, b)`` is zero.
+   nonzero *a* and *b*.  If either *a* or *b* is zero then ``lcm(a, b)`` is zero.
 
    .. versionadded:: 3.9
 

From 2db3ca75e4203da7d876c7fa5e00fd59b9ad3034 Mon Sep 17 00:00:00 2001
From: ananthan-123 <60189117+ananthan-123@users.noreply.github.com>
Date: Mon, 17 Feb 2020 08:05:41 +0530
Subject: [PATCH 83/83] Changed nonzero to both

---
 Doc/library/math.rst | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Doc/library/math.rst b/Doc/library/math.rst
index af00b2adb10174..d8ac35256d1b4b 100644
--- a/Doc/library/math.rst
+++ b/Doc/library/math.rst
@@ -140,7 +140,7 @@ Number-theoretic and representation functions
 
    Return the least common multiple of integers *a* and *b*.  The value of
    ``lcm(a, b)`` is the smallest nonnegative integer that is a multiple of
-   nonzero *a* and *b*.  If either *a* or *b* is zero then ``lcm(a, b)`` is zero.
+   both *a* and *b*.  If either *a* or *b* is zero then ``lcm(a, b)`` is zero.
 
    .. versionadded:: 3.9