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Let there be two natural numbers n,m.

let there be d = greatest common divisor of m and n - gcd(m,n)

and l = least common multiple of m and n - lcm(m,n)

I need to prove that CnXCm isomprphic to ClXCd (Cm Cn Cl Cd are all cyclic groups)

I have tried to see what happens if I look at m and n as products of prime numbers but I am kind of stuck around that idea without knowing where to take it.

I also think I should use the fact that gcd(m,n)*lcm(m,n) = m*n but also, can't figure out where to take it where to take it.

Another thing, if the gcd(m,n) = 1 I know that CmXCn is cyclic and the order of it is mn. I thought maybe this fact could help me somehow (m*n = l*d), but I don't know how, because it is possible that gcd(m,n) > 1

can somebody push me towards the right path to solution?

thanks!