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Possible Duplicate:
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

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    There is an explicit formula for $\varphi(n)$ in terms of the prime divisors of $n$. Using that should be pretty straight forward here. See http://en.wikipedia.org/wiki/Euler's_totient_function2012-04-16

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