Finding The Least Common Multiple

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So, I take it that your math teacher has been throwing around the term LCM,and you're needing to figure out what in the world is an LCM, and why you even need to bother with an LCM. Am I right?  Or maybe you just thought it was an acronym for Lost Cause in Mathematics.  I assure you, that is not the case, and I sure hope you don't believe you are a lost cause.  Let me also tell you that LCM stands for Least Common Multiple.

Relieved?  Good.

First of all, what is a multiple?

A multiple is the number you get when you multiply the number by another number (0, 1, 2…).

WHY DO I NEED TO KNOW HOW TO FIND THE LEAST COMMON MULTIPLE (LCM)?

Oh yes...the infamous "why" question.  There is a purpose, I promise:

When adding or subtracting fractions, you need to make sure that the denominators are the same before you can begin.  By first finding the Least Common Multiple, or the LCM, you will be able to accomplish this task.

FINDING THE LEAST COMMON MULTIPLE:

Let's just say that our denominators are 4 and 6. Your mission?  Find the multiples they have in common. You should list the first 10 multiples of the two numbers.  Like this:

As you can see, 4 and 6 have the following multiples in common:

12, 24, 36

Finally, put a square around the smallest multiple that the two numbers have in common:

The number 12 is the Least Common Multiple (LCM) of the numbers 4 and 6.  This is also called the Lowest Common Denominator (LCD).

Why don't you try?  See if you can find the LCM of the numbers 4 and 5.  Scroll down for the answer:

Drumroll, please!

Was your answer 20?  Great job!

Did you know you can also try this with 3 different numbers?  Try it with the numbers 4, 6, and 12.  What did you get?

Can I get another drumroll?  Thanks!

Did you get the answer 12?  

Superb! (If your answer was  not 12, check out my instructions above one more time and try to figure out what went wrong. Better, yet--use my comment section and I will help you!)