Coprimes and Congruence

Question

I need help getting a proof, I don't want solution to the problem just help guiding me to complete the proof.

Suppose $m,n$ are coprime, Prove that $a \equiv b \mod{mn}$ if and only if:

$a \equiv b \mod{m}$, and

$a \equiv b \mod{n}$.

Answer 1

HINT $$a=mk\\b=mt\\a=np\\b=nl$$