Definition:Lowest Common Multiple

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.