Definition:Lowest Common Multiple/Integers/Definition 2

Definition
Let $a, b \in \Z$ be integers such that $a b \ne 0$.

Then the lowest common multiple of $a$ and $b$ is the (strictly) positive integer $m$ which satisfies:
 * $(1): \quad a \divides m$ and $b \divides m$
 * $(2): \quad $If there exists $c \in \Z_{>0}$ such that $a \divides c$ and $b \divides c$, then $m \le c$

where $\divides$ denotes divisibility.

Also see

 * Equivalence of Definitions of Lowest Common Multiple