Why Find the LCM?

Date: 10/07/98 at 20:35:07
From: Karen Oldham
Subject: LCM

The question is not how to get the answer but why. I am the mother of 
four and one of the older children has to find the LCM of a group of 
numbers such as 15, 18, 21. We have no problem finding the answer, but 
where do you use this and how is it applied to real life? I guess I 
need to know what to say when I get the "Why do I have to do this!?"  
I just feel it helps to know. I never did. 

Thanks so much,
What a wonderful service!
Karen

Date: 10/08/98 at 17:00:34
From: Doctor Peterson
Subject: Re: LCM

Hi, Karen. Some of these "why" questions don't have a specific answer, 
because even if you didn't ever use them, some things we teach are 
worth learning just for the intellectual exercise they give. But the 
LCM has two purposes I can think of.

One your children should already have some feel for: they are needed to 
work with fractions. When you add or subtract fractions with different 
denominators, such as 1/15 + 1/18 + 1/21, you have to find a common 
denominator, something that is a multiple of all of them. Now, you 
could just multiply the three denominators, and that makes a perfectly 
good denominator to use, but it's much larger than it has to be, and 
makes you do a lot of extra work, not only to multiply and add bigger 
numbers, but then to simplify the resulting fraction. The work of 
finding an LCM saves a lot of work later on. (A lot of math is that way 
- what seems like a difficult task is really a shortcut for something. 
Mathematicians can be really lazy.)

Now that we have calculators, do we still need to worry about this? 
Well, for some purposes the decimals that calculators handle well 
aren't precise enough, and you have to work with fractions. If you 
didn't use the LCM, you might end up with numbers too big for the 
calculator to handle. That's probably rare, but it illustrates the 
second purpose I can see: that knowing LCMs builds an understanding of 
how numbers work, which can help people to use calculators and other 
tools more knowledgeably.

That may not convince the kids, but maybe it can convince you enough 
that you can say "yes" and mean it.

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