algebra with order.

hello sir~

i know the next contents.

let G be an abelian group and
let H and K be finite cyclic subgroups with |H|=r and
|K|=s.

if H=<a>, K=<b>, |ab| = lcm(r,s).

------------------------------------------------
if
G be an group.
|<a>| =r, |<b>| = s for some a, b in G.
ab = ba.

then, |ab| = lcm(r,s).


is this possible ?


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