I need help proving that if $m|a \lor m|b \Rightarrow m|ab$.
I was thinking that $m|a$ and $m|b$ is equivalent to $a = km$ and $b = lm$. Thus $ab = (kl)m^2$. Since this is a multiple of $m$ then $m|(kl)m^2$ and $m|ab$. But I'm not sure if that proves it - also with the $\lor$ in the premise.
Any advice or hints would be greatly appreciated.