CONFIDENTIAL 1

LEAST COMMON MULTIPLE

CONFIDENTIAL 2

• Find the prime factorization of each number:

1) 36 = 2 x 2 x 3 x 3

2) 76 = 2 x 2 x 19

3) 105 = 3 x 5 x 7

4) 145 = 5 x 29

Revision

CONFIDENTIAL 3

• A Multiple of a number is the product of the number and any whole number.

• For example, the multiples of 8 and 4 are listed below:

0 x 8 = 0 0 x 4 = 0

1 x 8 = 8 1 x 4 = 4

2 x 8 = 16 2 x 4 = 8

3 x 8 = 24 3 x 4 = 12

MULTIPLE

Multiples of 8 Multiples of 4

CONFIDENTIAL 4

• In the multiples of 8 and 4 - 0, 8, 16 and 24 are multiples of both 4 and 8. These numbers are common multiples of 4 and 8. The smallest number other than 0 is the Least Common Multiple.

Multiples of 4: 0, 4, 8, 12, 16, 20, 24, ……….

Multiples of 8: 0, 8, 16, 24, 32, 40, 48,……….

COMMON MULTIPLE & LEAST COMMON MULTIPLE (LCM)

The least of the common multiples of 4 and 8, other than 0 is 8

CONFIDENTIAL 5

Method - 1

• To find the LCM of two or more numbers, you can make a list

CONFIDENTIAL 6

Find the LCM by Making a List

Example - 1

Find the LCM of 6 and 12 by making a list.

Step 1 List the non-zero multiples.

multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60

multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120

Step 2 Identify the LCM from the common multiples.

The LCM of 6 and 12 is 12

CONFIDENTIAL 7

Try to do it now!!!

Find the LCM of 4 and 16 by making a list:

Multiples of 4: 4, 8, 12, 16, 20, 24, 32, 26, 40, 44, 48, 52….

Multiples of 16: 16, 32, 48, 64, 80, ……

Common multiples are: 16, 32, 48,…..

Least Common Multiple is 16

CONFIDENTIAL 8

Method - 2

• Prime Factors can also be used to find the LCM.

CONFIDENTIAL 9

Example - 2• Find the LCM of 15 and 25 by using prime factors:

Step 1 Write the prime factorization of each number.

15 25

3 x 5 5 x 5

Step 2 Identify all common prime factors

15 = 3 x 5

25 = 5 x 5

Step 3 Find the product of the prime factors using each common prime factor once and any remaining factors. The LCM is 3 x 5 x 5 =75

Take only one 5

CONFIDENTIAL 10

your turn

• Find the LCM of each set of numbers:

• 4 and 7

4 7

7 X 1 2 X 2

4 = 2 x 2 7 = 7 x 1;

Since there are no common factors, multiply all factors

i.e LCM = 2 x 2 x 7 x 1 = 28

CONFIDENTIAL 11

Have A Break

CONFIDENTIAL 12

Practice Problems

• Find the LCM of each set of numbers by making a list.

1. 2 and 10 LCM = 10

2. 8 and 36 LCM = 72

3. 4 and 5 LCM = 20

4. 5 and 13 LCM = 65

5. 3, 5 and 7 LCM = 105

CONFIDENTIAL 13

More Practice Problems

• Find the LCM by using prime factors:

1. 16 and 20 LCM = 80

2. 27 and 18 LCM = 54

3. 15 and 18 LCM = 90

4. 8 and 28 LCM = 56

5. 12, 18 and 24 LCM = 72

CONFIDENTIAL 14

Use LCM to Solve a Problem

• In a class, chairs are placed in rows so that either 6 or 10 members are in each row. What is the least number of students that can be seated in the class

• Least number of students that can be seated in the class = LCM of 6 and 10

• Multiples of 6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60

• Multiples of 10 = 10, 20, 30, 40, 50, 60, …..

• Common multiples are: 30, 60, …

• LCM = 30

CONFIDENTIAL 15

Solve this!

• Columbus is planting his new garden. He knows he can plant all his roses by planting 12 or 15 rose bushes in every row. What is the least number of rose bushes he could have?

• Multiple of 12: 12, 24, 36, 48, 60, 72,….

• Multiples of 15: 15, 30, 45, 60, 75,….

• LCM of 12 and 15 = 60

i.e he will be able to plant 60 rose bushes

CONFIDENTIAL 16

REVIEW

• The smallest number other than 0 that is a multiple of two or more whole numbers is the LEAST COMMON MULTIPLE.

CONFIDENTIAL 17

WE WILL MEET YOU SOON WITH A NEW TOPIC