Least Common Multiple

In arithmetic and number theory, the least common multiple of two integers a and b, usually written lcm(a, b), is the smallest positive integer that both a and b divide into evenly; because division by zero is undefined this only makes sense when a and b are both nonzero, though some authors define lcm(a, 0) as 0 since 0 is the only common multiple of a and 0. The least common multiple of the denominators of two fractions is called the lowest common denominator and is used to add, subtract or compare fractions, and the same idea extends to the least common multiple of more than two integers, the smallest positive integer divisible by each of them.