Group, Cosets, Normal Group help

Hello,

Could you help me in solving this problem?

---- Let G group, and H, K subgroups of G. Prove that if [G:H]=h and

[G:K]=k then lcm(h,k)|[G:H$\displaystyle \cap$K] <= h.k and if H or K are

normal subgroups of G then

[G:H intersection K] | h.k ----

I could prove that [G:H$\displaystyle \cap$K] <= h.k but i cannot prove

lcm(h,k)|[G:H intersection K] and if H or K are normal subgroups of G

then

[G:H$\displaystyle \cap$K] | h.k

Pleas i really appreciate very much your help and i'm sorry for my bad english

Cheers,

RP