least_common_multiple.py

import unittest
from timeit import timeit


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

    >>> least_common_multiple_slow(5, 2)
    10
    >>> least_common_multiple_slow(12, 76)
    228
    """
    max_num = first_num if first_num >= second_num else second_num
    common_mult = max_num
    while (common_mult % first_num > 0) or (common_mult % second_num > 0):
        common_mult += max_num
    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 = [
        (10, 20),
        (13, 15),
        (4, 31),
        (10, 42),
        (43, 34),
        (5, 12),
        (12, 25),
        (10, 25),
        (6, 9),
    ]
    expected_results = [20, 195, 124, 210, 1462, 60, 300, 50, 18]

    def test_lcm_function(self):
        for i, (first_num, second_num) in enumerate(self.test_inputs):
            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(slow_result, self.expected_results[i])
                self.assertEqual(fast_result, self.expected_results[i])


if __name__ == "__main__":
    benchmark()
    unittest.main()