i'm reading Introduction to Analytic Number Theory, Tom M. Apostol and i have a doubt about an exercise in chapter 1. Follow the exercise:

Prove the following multiplicative property of the gcd:

$\displaystyle (ah,bk)=(a,b)(h,k)\left ( \frac{a}{(a,b)},\frac{k}{(h,k)} \right )\left ( \frac{b}{(a,b)},\frac{h}{(h,k)} \right )$

i already tried using Bezout identity and $\displaystyle (a,b)=\frac{a\cdot b}{[a,b]}$