Lesson 2 — Activity 1: Lowest Common Multiple (LCM)


Getting Ready


When you completed the last activity on scientific notation, you first practised writing multiples of 10 (100 = 10 x 10)

Multiples are the product (answer) of a known number and a whole number. For example, to find the first five multiples of the number 2, you would do the following:

  • 2 x 1 = 2
  • 2 x 2 = 4
  • 2 x 3 = 6
  • 2 x 4 = 8

  • 2 x 5 = 10

The multiples of 2 are: {2, 4, 6, 8, 10}


Try This:


What are the first five multiples of the number 3?


  • 3 x 1 = 3
  • 3 x 2 = 6
  • 3 x 3 = 9
  • 3 x 4 = 12
  • 3 x 5 = 15

The multiples of 3 are: {3, 6, 9, 12, 15}







Sometimes it is important to know what the lowest common number is between two different numbers.



For example, let's say you are having some friends over. You want everyone to get the same amount of snacks. You want to purchase chocolate bars that come in packages of 4 and drinks that comes in packages of 6.



How many packages of chocolate bars and drinks do you need to buy so that you have the same amount of each?

A 4 pack of Twix chocolate bars

A 6 pack of Cola drinks
Images courtesy of www.imagesgoogle.com

You could make a table and look for a common number.

Product 1 Package
2 Packages
 3 Packages
 4 Packages
Chocolate Bars
 
 4  8  12  16
Drinks

 6 12
 18 24

Looking at the table, you can see that 12 is the common number.
This means you need to buy 3 packages of chocolate bars and 2 packages of drinks.


Making a table like this can be time-consuming. Another way is to use the lowest common multiple (LCM).

Calculating the lowest common multiple is similar to the chart but much faster. All you do is list the multiples of each number until you find a common number. This common number is the lowest common multiple.


Let's look at the numbers 3 and 5. What is the lowest common multiple for 3 and 5?


The easiest way is to list the multiples like this:

  • 5: {5, 10, 15, 20}
  • 3: {3, 6, 9, 12, 15}

The LCM for 3 and 5 is 15.


  • List the multiples of the larger number first. Start with the first five multiples.
  • Then list the multiples of the lower number right below until you find a common number.
  • You may need to increase the length of the list of multiples for the large number if you don't find a common multiple fairly quickly.



Let's try another one:

 2 and 7

7: {7, 14, 21, 28, 25}


2: {2, 4, 6, 8, 10, 12, 14}


The LCM for 2 and 7 is 14.

Try This:


What about 2 and 6?


  • First, list the multiples for 6.
  • Then, list the multiples for 2 until you come to a common number.


6: { 6, 12, 18, 24, 30}


2: {2, 4, 6}


The LCM for 2 and 6 is 6.


 


Digging Deeper


Click here for more information on finding the lowest common multiple.




Digging Deeper


Click here to try your hand at a game to find the lowest common multiples.