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 $a \mathrel \backslash m$ and $b \mathrel \backslash m$.

This $m$ is called the lowest common multiple (LCM) of $a$ and $b$, and denoted $\operatorname{lcm} \left\{{a, b}\right\}$.

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 $a b \ne 0$.

Also known as
The lowest common multiple can also be seen as least common multiple.

Also see

 * Greatest Common Divisor
 * Existence of Lowest Common Multiple