from .math_gcd_lcm_gcd import gcd

_MAX_SAFE = 9007199254740991


def lcm(a: int, b: int) -> int:
    """Least common multiple, never negative; 0 when either input is 0."""
    g = gcd(a, b)
    if g == 0:
        return 0
    # Divide before multiplying: a * b overflows long before the lcm does.
    result = abs(a) // g * abs(b)
    if result > _MAX_SAFE:
        raise ValueError("the lcm of %d and %d exceeds 2^53 - 1" % (a, b))
    return result