Algebra: abelian finite group

12 i) Let A be an abelian finite group, and let a,b be elements in A.

Show that the order of ab is a divisor of the lcm( (ord(a), ord(b) ).

Okay, I tried:

It follows by definition that all elements in A have finite order.

lcm( (ord(a), ord(b) ) = x, so x divides ord(a) and x divides ord(b).

I have to show that the order of ab is a divisor of x.

My first thought:

I have to show that "the order of ab" is a divisor of "x".

Since "x" divides both ord(a) and ord(b) it follows:

ord(a) / x / order of ab = ord(a) / (x*order of ab)

ord(b) / x / order of ab = ord(b) / (x*order of ab)

Well, I guess I'm going the wrong way because it doesn't make sense.

Can someone help me get further?

Tnx. & sorry if I got the topic ("pre-algebra and algebra" wrong!)