It is known that $(m, n)>1$. Which is greater, $\varphi(m n)$ or $\varphi(m) \varphi(n)$? For the definition of the function $\varphi(n)$, see problem $\underline{60758}$.
For each prime number $p$ that is a divisor of both $m$ and $n$, in the number $\varphi(m n)$, the corresponding factor is $1 - 1 / p$, while in the number $\varphi(m) \varphi(n)$, the factor is

$(1-1 / p)^{2}$. Since $1-1 / p\varphi(m) \varphi(n)$.

## Answer

$\varphi(m n)$.