\begin{definition}[Definition:Lowest Common Multiple/Integers]
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 $a b \ne 0$.
\end{definition}