Prove or disprove that If $a\mid c$ and $b\mid c$, then $ab \mid c$.

Question

So I am not really sure what to do. I know by the definition of divisibility there must exist some integers $k$ and $l$ such that

$$ c= ak \  \text{ and  } \ c=bl $$

But now I am stuck and have no clue where to go from here...

I need to show that $c=ab(\text{some integer})$, for it to be divisible, but I do not see the path to take.

Answer 1

If $a= b = c > 1$ then $a|c, b|c, ab \not\mid c$.