# Did I just come up with this?

## Main Question or Discussion Point

Well, last summer I had a lot of time on my hands, and I would stay up late just randomly playing with math and numbers to kill time. After playing around with them long enough, I seem to have come up with a theorem/axiom/postulate (I don't know the terminology). I never really thought that I had come up with anything new until I had a look at my notebook today, and started Googling. Perhaps I wasn't trying the right keywords, but I can't find anything like this online. Now that I think about it, I seem to remember writing a program to prove this true, and it ended up working. I've since reformatted that computer (installed my mom's new OS).

Anyways, it's not really a big deal or anything, and I doubt it's really useful, but:

"If the absolute value of a minus b is equal to one, then the least common multiple of a and b is equal to ab."

or

If |a-b| = 1 Then LCM(a,b) = ab

I'm sure something like this is already in existence, but I can't seem to find it... Can anybody else?

I'm afraid what you've come up with isn't new-- your statement says that the least common multiple of two consecutive integers is their product. You can see this by looking at the formula for the least common multiple of two numbers $$lcm(a,b)=\frac{ab}{gcd(a,b)}$$. Since a and b are consecutive, gcd(a,b)=1, which yields the result.