diff --git a/maths/least_common_multiple.py b/maths/least_common_multiple.py index a5c4bf8e3625..9eca5ae97942 100644 --- a/maths/least_common_multiple.py +++ b/maths/least_common_multiple.py @@ -6,7 +6,7 @@ def least_common_multiple_slow(first_num: int, second_num: int) -> int: """ - Find the least common multiple of two numbers. + Find the least common multiple (LCM) of two integers. Learn more: https://en.wikipedia.org/wiki/Least_common_multiple @@ -14,8 +14,13 @@ def least_common_multiple_slow(first_num: int, second_num: int) -> int: 10 >>> least_common_multiple_slow(12, 76) 228 + >>> least_common_multiple_slow(0, 5) + 0 """ - max_num = first_num if first_num >= second_num else second_num + if first_num == 0 or second_num == 0: + return 0 + + max_num = max(abs(first_num), abs(second_num)) common_mult = max_num while (common_mult % first_num > 0) or (common_mult % second_num > 0): common_mult += max_num @@ -24,14 +29,22 @@ def least_common_multiple_slow(first_num: int, second_num: int) -> int: def least_common_multiple_fast(first_num: int, second_num: int) -> int: """ - Find the least common multiple of two numbers. + Find the least common multiple (LCM) of two integers. + + Uses the relationship between LCM and GCD: https://en.wikipedia.org/wiki/Least_common_multiple#Using_the_greatest_common_divisor - >>> least_common_multiple_fast(5,2) + + >>> least_common_multiple_fast(5, 2) 10 - >>> least_common_multiple_fast(12,76) + >>> least_common_multiple_fast(12, 76) 228 + >>> least_common_multiple_fast(0, 5) + 0 """ - return first_num // greatest_common_divisor(first_num, second_num) * second_num + if first_num == 0 or second_num == 0: + return 0 + + return abs(first_num // greatest_common_divisor(first_num, second_num) * second_num) def benchmark(): @@ -59,8 +72,9 @@ class TestLeastCommonMultiple(unittest.TestCase): (12, 25), (10, 25), (6, 9), + (0, 5), ) - expected_results = (20, 195, 124, 210, 1462, 60, 300, 50, 18) + expected_results = (20, 195, 124, 210, 1462, 60, 300, 50, 18, 0) def test_lcm_function(self): for i, (first_num, second_num) in enumerate(self.test_inputs):