Least Common Multiple

Date: 11/5/95 at 17:47:10
From: Anonymous
Subject: Lowest Common Multiplier

What is the lowest common multiplier of 8, 12 and 36?

I'm not even sure what a lowest common multiplier is.  I think 
it's the smallest integer which can be divided by any member of 
the set without leaving a remainder, but I'm not sure.  The 
internet sure has a lot of cross-referencing on sites where one 
can get information on Math but very little areas where 
mathematics itself is discussed. You provide a valuable service.

Date: 11/12/95 at 14:27:34
From: Doctor Ken
Subject: Re: Lowest Common Multiplier

Hello!

Actually, I'm not surprised that you don't know what a "lowest 
common multiplier" is.  There's a term called "least common 
multiple" that is exactly what you describe: it's the smallest 
integer that can be divided evenly by each member of the set.  
"Multiplier" means "something you can multiply by," so "lowest 
common multiplier" would be the smallest number that you can 
multiply all of the given numbers by.  Doesn't make too much 
sense.

My favorite way to find the least common multiple (LCM) of a bunch 
of  numbers is to write them in prime factored form, then take the 
greatest  power on each prime.  For instance, to get the LCM of 
168, 98, and 45,  I'd write them as  2^3 * 3 * 7,   2 * 7^2,  and  
5 * 3^2, and then take  the biggest powers:

2^3 * 3^2 * 5 * 7^2 = 17640.

-Doctor Ken,  The Geometry Forum