The least common multiple (LCM) of 2 numbers is the smallest number that they both divide evenly into.
e.g.:
LCM(8,10)=40
LCM(17,11)=187

For any integer n, show that LCM(9n + 8, 6n + 5) = 54n^2 + 93n + 40.

(In reply to re: Proof by Steve Herman)

I now see the flaw in my "proof". In the third paragraph I claim that the two numbers differ by 3n + 3, and that that is divisible by 3 and by n.  Of course it's not actually divisible by n, but rather by n + 1.

Posted by Charlie on 2013-11-20 09:46:52