Least Common Multiple

Algebra Seminar2012-2013

What is LCM?

• LCM stands for Least Common Multiple• LCM is used to find a common denominator

for two fractions in order to compare them.• LCM is defined as: the smallest number

that both numbers are factors of.

• Lets watch a short video from www.unitedstreaming.com on LCM.

Finding the LCMLeast Common Multiple (LCM):

Method 1: Make a list of multiples

Ex: Find the LCM of 4 and 9

9: 9, 18, 27, 36, 45,

4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40 44

36 is the LCM of 4 and 9

More Examples of LCMEx: Find the LCM of 10 and 12

10:12:

10, 20, 30, 40, 50, 60, 70, 80, 90, 10012, 24, 36, 48, 60, 72, 84, 96, 108

60 is the LCM of 10 and 12

Ex: Find the LCM of 6 and 8

6:8:

6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 728, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88

24 is the LCM of 6 and 8

Tips for finding the Least Common Multiple

1. Make a list of multiples for each number2. Look for the smallest number they have in common3. If you are looking for the LCM of more than two numbers make more lists. The LCM must be common to ALL of the numbers.

5 = 5, 10, 15, 20, 25, 30, 35 6 = 6, 12, 18, 24, 30, 36 10 = 10, 20 , 30, 40, 50 , 60

Put the following fractions in order from greatest to least without using a calculator:

6

1,9

5,

12

7,3

2

Using the LCM to Put Fractions in Order

Without a calculator, we cannot change the fractions to decimals. We will have to use LCM.

Step 1: Find the LCM of the denominators

Using the LCM to Put Fractions in Order

3: 3, 6, 9, 12, 15, 18, 21, 24, 27

30, 33, 36, 39, 42 …

6: 6, 12, 18, 24, 30, 36, 42, 48…

LCM = 36

The LCM of 6, 12, 9, and 3 is….

12: 12, 24, 36, 48 …

9: 9, 18, 27, 36, 45 …

Step 2: Write equivalent fractions.

36x 6

x 6 6 12

736x 3

x 3 21

9

536x 4

x 4 20 3

236x 12

x 1224

Greatest to Least

Step 3: Compare the numerators

6

1

36 6

12

73621

9

53620

3

23624

Put the Fractions in Order

Now try this one.

The correct answer is:

Here are some more to try.