Let m and n be any two positive integers. Then prove that : Φ(mn) = Φ{ (m, n)Φ[m, n] } where (m,n)=the g.c.d.of m and n and [m, n]= the l.c.m of m and n
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1See https://math.stackexchange.com/questions/1252244/ifmnbepositiveintegersprovethatphimnphimnphimnwh – lab bhattacharjee Dec 06 '17 at 11:16

$m = p, n = p^2, (m,n) = p, [m,n] = p^2$, $\phi(p^3) \ne \phi(p) \phi(p^2)$. @labbhattacharjee – reuns Dec 06 '17 at 12:07

Not even mentioning the case $m=n$... – reuns Dec 06 '17 at 12:11

The correct "duplicate" is thisone https://math.stackexchange.com/q/114841/276986 – reuns Dec 06 '17 at 12:13