Show that if $\displaystyle a\mid{c}$ and $\displaystyle b\mid{c}$ then $\displaystyle ab\mid{c}$

I got started and have Let c=ae and c=bd where d and e are integers.

c=ae=bd and a and b are not equal then e=b and d=a thus $\displaystyle ab\mid{c}$ where the result would be 1.

I am pretty sure my logic is really messed up though.