Definition:Lowest Common Multiple/Integers

Definition
For all $a, b \in \Z: a b \ne 0$, there exists a smallest $m \in \Z: m > 0$ such that $a \divides m$ and $b \divides m$.

This $m$ is called the lowest common multiple of $a$ and $b$, and denoted $\lcm \set {a, b}$.

Note that unlike the GCD, where either of $a$ or $b$ must be non-zero, for the LCM both $a$ and $b$ must be non-zero, which is why the stipulation $a b \ne 0$.

General Definition
This definition can be extended to any (finite) number of integers.

Also see

 * Definition:Greatest Common Divisor of Integers
 * Existence of Lowest Common Multiple