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Prove that G/(M[itex]\bigcap[/itex]N)[itex]\cong[/itex](G/M)x(G/N).

I tried coming up with an isomorphism from G to (G/M)x(G/N) such that the kernel is M[itex]\bigcap[/itex]N, so that I can use the fundamental homomorphism theorem.

I tried f(a) = (aM, aN). It is an homomorphism and M[itex]\bigcap[/itex]N is the kernel but I'm having a hard time showing it is onto.

I would appreciate any help.

Thank you