Prove $\gcd(ka,kb) = k*\gcd(a,b)$

Question

For all $k > 0,\ k\in \Bbb Z$ . Prove $$\gcd(k*a,\ k*b) = k *\gcd(a,\ b)$$

I think I understand what this wants but I can't figure out how to set up a formal proof. These are the guidelines we have to follow

Answer 1

Hint: Start with the fact that $\gcd(k a, k b)$ is the minimal positive value of $s k a + t k b$, and factor out $k$.