if $a\mid x$ and $b\mid x$ and $\gcd(a,b) = 1$, prove that $a\cdot b\mid x$
Well, I've started by saying that $x = q_1a$ and $x = q_2b$, and I know that $a,b$ are prime numbers. And, I'm not sure how to proceed from here.
Edit: The answer here is better than in the posts listed here