Let $m_1,m_2\ge1$ be such that $\gcd(m_1,m_2) \ne 1$. Argue that $\phi(m_1*m_2)$ is strictly less that $\phi(m_1)*\phi(m_2)$.
What I have so far:
By example (which I'm not sure if that's how he wants the answer... ):
$$\phi(5*20)=\phi(100)=(2^2-2)*(5^2-5)=40$$
$$\phi(5)=4$$
$$\phi(20)=(2^2-2)*(4)=8$$
$$8*4=32$$
Where $32 \lt 40$. Is this a sufficient way to answer this question? Could someone maybe give me a hint as to how to how I could answer the question in a way other than by example?