Let $a$ and $b$ commute. If $m$ and $n$ are relatively prime, then ord($ab$) = $mn$.
$\operatorname{ord}(u)=r,\,\operatorname{ord}(v)=s$ $\,\Rightarrow\,\operatorname{ord}(uv)=rs\,$ if $\,r,s\,$ (co)primes