More efficient least common multiple. (#2281)

* More efficient least common multiple.

* lowest -> least

* integer division

* Update least_common_multiple.py

Co-authored-by: Christian Clauss <cclauss@me.com>

maths/least_common_multiple.py

@@ -1,14 +1,16 @@
 import unittest
+from timeit import timeit
 
 
-def find_lcm(first_num: int, second_num: int) -> int:
-    """Find the least common multiple of two numbers.
+def least_common_multiple_slow(first_num: int, second_num: int) -> int:
+    """
+    Find the least common multiple of two numbers.
 
     Learn more: https://en.wikipedia.org/wiki/Least_common_multiple
 
-       >>> find_lcm(5,2)
+    >>> least_common_multiple_slow(5, 2)
     10
-       >>> find_lcm(12,76)
+    >>> least_common_multiple_slow(12, 76)
     228
     """
     max_num = first_num if first_num >= second_num else second_num
@@ -18,6 +20,52 @@ def find_lcm(first_num: int, second_num: int) -> int:
     return common_mult
 
 
+def greatest_common_divisor(a: int, b: int) -> int:
+    """
+    Calculate Greatest Common Divisor (GCD).
+    see greatest_common_divisor.py
+    >>> greatest_common_divisor(24, 40)
+    8
+    >>> greatest_common_divisor(1, 1)
+    1
+    >>> greatest_common_divisor(1, 800)
+    1
+    >>> greatest_common_divisor(11, 37)
+    1
+    >>> greatest_common_divisor(3, 5)
+    1
+    >>> greatest_common_divisor(16, 4)
+    4
+    """
+    return b if a == 0 else greatest_common_divisor(b % a, a)
+
+
+def least_common_multiple_fast(first_num: int, second_num: int) -> int:
+    """
+    Find the least common multiple of two numbers.
+    https://en.wikipedia.org/wiki/Least_common_multiple#Using_the_greatest_common_divisor
+    >>> least_common_multiple_fast(5,2)
+    10
+    >>> least_common_multiple_fast(12,76)
+    228
+    """
+    return first_num // greatest_common_divisor(first_num, second_num) * second_num
+
+
+def benchmark():
+    setup = (
+        "from __main__ import least_common_multiple_slow, least_common_multiple_fast"
+    )
+    print(
+        "least_common_multiple_slow():",
+        timeit("least_common_multiple_slow(1000, 999)", setup=setup),
+    )
+    print(
+        "least_common_multiple_fast():",
+        timeit("least_common_multiple_fast(1000, 999)", setup=setup),
+    )
+
+
 class TestLeastCommonMultiple(unittest.TestCase):
 
     test_inputs = [
@@ -35,10 +83,13 @@ class TestLeastCommonMultiple(unittest.TestCase):
 
     def test_lcm_function(self):
         for i, (first_num, second_num) in enumerate(self.test_inputs):
-            actual_result = find_lcm(first_num, second_num)
+            slow_result = least_common_multiple_slow(first_num, second_num)
+            fast_result = least_common_multiple_fast(first_num, second_num)
             with self.subTest(i=i):
-                self.assertEqual(actual_result, self.expected_results[i])
+                self.assertEqual(slow_result, self.expected_results[i])
+                self.assertEqual(fast_result, self.expected_results[i])
 
 
 if __name__ == "__main__":
+    benchmark()
     unittest.main()