Least Common Multiple

Date: 09/29/2001 at 15:19:22
From: Rachel
Subject: Least Common Multiple

What is the least common multiple of 11, 13, and 17?  I've already 
tried the calculator to try to find it, but that doesn't seem to be 
working, because I can't find any LCM of 11, 13, and 17 that is not 
11 x 13 x 17.  Please help!

Date: 09/29/2001 at 16:33:39
From: Doctor Jodi
Subject: Re: Least Common Multiple

Hi Rachel,

Excellent question.

In fact, 11 x 13 x 17 IS the LCM of 11, 13, and 17.

Often when you want to find the LCM, there are common factors. For 
instance, what's the LCM of 4 and 6?

One way to find it is to write 4 = 2 x 2 and 6 = 2 x 3. Then you 
take the LCM as 2 x 2 x 3. So the LCM of 4 and 6 is 12. You know 
that the LCM can't be smaller, because two 2s have to divide it 
(since 2 x 2 = 4) and 2 and 3 have to divide it (since 2 x 3 = 6). 
Does this make sense?

Let's try the same trick with 11, 13, and 17.

First of all, how can we factor each of them? 

   11 = 1 x 11
   13 = 1 x 13 
   17 = 1 x 17

This is the ONLY way to factor these numbers. A number that has just 
two factors - one and itself--is called prime. 11, 13, and 17 are 
prime numbers.

So what will the LCM of 11, 13, and 17 be? 1, 11, 13, and 17 must all 
divide it. So we have to take their product: 

   1 x 11 x 13 x 17 = 11 x 13 x 17 = 2431

Does this make sense? Write back if you have more questions.

- Doctor Jodi, The Math Forum
  http://mathforum.org/dr.math/