Strayer Elementary Number Theory 1. 5. 78.

This one sucks. I think it may have came a little easier to the readers of Strayer's number theory book if more exercises on the l.c.m. of more than two integers had came before this problem. Anyways, the l.c.m. of more than two variables seems to be the most elementary way of tackling this problem, yet not much is known about the l.c.m. of more than two variables by the time we get to Ex. 78... so you have to prove anything you need yourself.

I got stuck. I'm glad to say I was kinda on the right path... I knew it came down to odd numerators vs. even denominators, just by computing and looking at some early values of n. But I couldn't piece it together anymore than that, especially being foggy on the l.c.m. of more than two integers. Anyways thanks to Quora on this one, although I took the time to flesh my solution out a bit and add an obvious but useful Lemma.