## Euler's Totient Function Proving

I need some help/hints on how to prove this statement. I don't know where to start!

Prove that if m and n are positive integers such that m|n, then φ(mn) = mφ(n).

Thanks
 It's a direct consequence of Euler's formula: $$\phi\left(n\right)=n(1-\frac{1}{p_1})(1-\frac{1}{p_2}) \cdots (1-\frac{1}{p_k})$$ Because the hypothesis implies that the prime factorization of m has the same factors as n. Or you can count the numbers that are coprime with nm in $$\left\{1,\ldots,mn\right\}$$ and prove that there are as many as the ones that are coprime with n in $$\left\{1,\ldots,n\right\}$$.