Is $\phi (k_1) + \phi (k_2)+\phi (k_3) +...\phi (k_n)=gcd(m, n) $ ? k is divisor of m and n

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Let $k_1, k_2, k_3,\dots ,k_n$ be positive divisors of $m$ and $n$. Can you prove or disprove the following $$\varphi (k_1) + \varphi (k_2)+\varphi (k_3) +\dots+\varphi (k_n)=\gcd(m, n).$$