Lesson 7 – Finding LCM Using Prime Factors.

Objectives:

At the end of the lesson, students should be able to find the least common multiples of numbers using their prime factors.

There are different ways of finding the LCM of numbers. These include the factor tree, list method and ladder method.

Example: 1

Find the LCM of the following pairs of numbers by finding the prime factors using the factor tree method.
a. 14 and 18
b. 24 and 30

Solution

LCM = 2 X 2 X 2 X 3 X 5

= 2³ X 3 X 5

= 120

Example: 2

Using the list method, find the LCM of the following sets of numbers.
a. 9 and 12
b. 18 and 24
 
Solution
a. 9 = 3 x 3

12 = 2 x 2x 3

L.C.M = 2 X 2 X 3 X 3

L.C.M = 36

 
b. 18 and 24
18 = 2 x 3 x 3

24 = 2 x 2 x 2 x 3

L.C.M = 2³ x 3²
C. M = 8 x 9 = 72

Example: 3

Find the LCM of these sets of numbers using the ladder method.
a. 12 and 20
b. 14, 18 and 24
 

Solution

LCM = 2 X 2 X 3 X 5 = 2² X 3 X 5 = 60

Note: from the examples, note that the numbers are divided by prime factors until each number is reduced to 1.

Unit 8 Lesson 7: Exercise 1

Find the LCM of the following pairs of numbers using any method.

1. 12 and 24
2. 28 and 48
3. 36 and 54
4. 40 and 64
5. 24 and 32
6. 45 and 72
7. 28 and 40
8. 36 and 48
9. 100 and 120
10. 120 and 108

Answers

Unit 8 Lesson 7: Exercise 2

Find the LCM of the following sets of numbers using any method.

1. 18 and 30
2. 27 and 45
3. 40 and 56
4. 54 and 90
5. 45 and 70
6. 12, 18 and 30
7. 15, 45 and 75
8. 18, 27 and 45
9. 36, 48 and 60
10. 54, 72 and 90

Answers

 

 

 

Unit 8 Lesson 9: Exercise 3

Find the HCF and LCM of these sets of numbers.

1. 30 and 39
2. 20 and 40
3. 12 and 36
4. 42 and 64
5. 32 and 72
6. 12, 18 and 24
7. 24, 30 and 36
8. 36, 52 and 78
9. 20, 40 and 60
10. 100, 120 and 150

Answers