Euler Phi Function is not Completely Multiplicative

Theorem
The Euler $\phi$ function is not a completely multiplicative function.

That is, it is not always the case that:


 * $\map \phi {m n} = \map \phi m \map \phi n$

where $m, n \in \Z_{>0}$.

Proof

 * Proof by Counterexample

Hence we see:
 * $6 \times 10 = 60$

byt:
 * $\map \phi 6 \times \map \phi {10} \ne \map \phi {60}$