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Proof of a formula involving Euler's totient function.

For positive integers $m$ and $n$ where $d=gcd(m,n)$, show that $$\phi(mn) = \phi(m)\phi(n)\frac{d}{\phi(d)}$$

This is just the generalization of the multiplicative property of *phi* function.I have tried to solve this in the same way as the proof of multiplicative property but couldn't get far.Please help.