Project Euler Problem 5
The smallest number that can be divided by a set of numbers without any remainder is also known as the least common multiple, which can be calculated directly using the greatest common divisor (gcd).

The least common multiple of a, b:

lcm(a, b) = a * b / gcd(a, b)


The least common multiple of a, b, c:

lcm(a, b, c) = lcm(a, lcm(b, c))


You could generalize this to more numbers.