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> How do I prove that if $a|c$ and $b|c$ then $ab | c$ if $\gcd(a,b) = 1$?
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I got stuck with the following steps:

1. Express $c = ma = nb$ for some $m, n$ integers.
2. Multiply together the $2$ expressions to get $c^2 = mn(ab)$

But I cannot show that $c = \frac{mn}{c}(ab)$ because $mn/c$ might not be an integer.

How do I use the result that $\gcd(a,b) = 1$?