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Proof of a formula involving Euler's totient function.

I have this interesting question that I have difficulty to prove.

I know that:

$ \gcd(a,b) = d $

And I need tho show that:

$ \varphi(ab) = d\varphi(a)\varphi(b) / \varphi(d) $

where $\varphi$ is Euler's totient function