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### 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

```
Associated Topics:
Middle School Division

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