Can anyone help me with this question, I don't know where to start?

If d = gcd(a,b). Show that phi(d)*phi(a*b) = d*phi(a)*phi(b)

I was thinking along the lines of unique factorization of a, b and d into primes, then somehow show that the two equations equal. The problem is I'm unsure how I should go about factorizing them to make it work out in the end. Any help is appreciated. Thanks