Prove that if $ \gcd(a,m) = 1 $ and $ a b \equiv a c ~ (\operatorname{mod} ~ m) $, then $ b \equiv c ~ (\operatorname{mod} ~ m) $.

Question

Problem. Prove that if $ \gcd(a,m) = 1 $ and $ a b \equiv a c \pmod m $, then $ b \equiv c \pmod m $.

I have $ m | a b - a c $, or $ m | a (b - c) $, and I know that if $ \gcd(a,m) = 1 $, then $ n | b - c $. I just don’t know what lemma I can use here.