Order of $xy$ in a group G

Question

I'm studying abstract algebra alone as my doctor needs a doctor haha. Ok, I'm studying about cyclic groups now. I read that:

if 2 elements $x$ and $y$ commute in a group $G$, then the order of $xy$ is a divisor of $l.c.m(o(x),o(y))$,

then I read that it's exactly equal to $l.c.m(o(x),o(y))$, so got confused. Can anybody explain this to me? Also, can anybody advise me to read some detailed lectures about cyclic groups, as I feel like if I need much more to be strong at this lesson.

Answer 1

See the answer which was accepted from the other post.