I have a problem where I have to prove that $\displaystyle \phi(nm)=\phi(m)\phi(n)$ where n and m are relatively prime and $\displaystyle \phi$ is Euler's totent.

I know that for the proof I must show that there is a bijection between $\displaystyle mn$ and $\displaystyle m \times n$ and I am having troubles doing that. Any help would be appreciated.