Prove: If $c \ge ab$ and $a|c$ and $b|c$ then $ab|c$.
If $a|c$ and $b|c$ then there are integers $p$ and $q$ such that
$ap=c$ and $bq=c$
All of my work has boiled down to substitutions, a lot of them. My intuition has been pointing towards the inequality, but I'm not sure how to implement it.
I've attempted manipulating a diophantine equation, but I'm not sure if I have enough prior results available to use anything like ax+cy=1.