bpo-39479:Add math.lcm() function: Least Common Multiple

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*.  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.
+
+   .. versionadded:: 3.9
+
+
 .. 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

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
 -------
 

Lib/test/test_math.py

@@ -974,6 +974,41 @@ def __index__(self):
                 with self.assertRaises(TypeError):
                     math.isqrt(value)
 
+    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)
+        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),
+                             16592536571065866494401400422922201534178938447014944)
+        x = 434610456570399902378880679233098819019853229470286994367836600566
+        y = 1064502245825115327754847244914921553977
+
+        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.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)
         self.ftest('ldexp(0,1)', math.ldexp(0,1), 0)

Misc/NEWS.d/next/Library/2020-02-04-13-47-16.bpo-39479.BN_mM9.rst

@@ -0,0 +1 @@
+Add func:`math.lcm` function: Least Common Multiple.

Modules/mathmodule.c

@@ -2016,6 +2016,60 @@ 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_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) {
+        return NULL;
+    }
+    b = PyNumber_Index(b);
+    if (b == NULL) {
+        Py_DECREF(a);
+        return NULL;
+    }
+    if (_PyLong_Sign(a) == 0 || _PyLong_Sign(b) == 0) {
+        Py_DECREF(a);
+        Py_DECREF(b);
+        return PyLong_FromLong(0);
+    }
+    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);
+    if (m == NULL) {
+        return NULL;
+    }    
+    ab = PyNumber_Absolute(m);
+    Py_DECREF(m);
+    return ab;
+}
+
+
 /*[clinic input]
 math.trunc
 
@@ -3361,6 +3415,7 @@ 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