Definition:Lowest Common Multiple

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

This is proved in Existence of Lowest Common Multiple.

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 $a b \ne 0$.

Note
Alternatively, $\operatorname{lcm} \left\{{a, b}\right\}$ can be found written as $\left [{a, b} \right]$.

This usage is not recommended as it can cause confusion.

It is also known as the least common multiple.