__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

= 2^{3} 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 = 2^{3} x 3^{2}

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 = 2^{2} 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.**

- 12 and 24
- 28 and 48
- 36 and 54
- 40 and 64
- 24 and 32
- 45 and 72
- 28 and 40
- 36 and 48
- 100 and 120
- 120 and 108

__Unit 8 Lesson 7: Exercise 2__

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

- 18 and 30
- 27 and 45
- 40 and 56
- 54 and 90
- 45 and 70
- 12, 18 and 30
- 15, 45 and 75
- 18, 27 and 45
- 36, 48 and 60
- 54, 72 and 90

__Unit 8 Lesson 9: Exercise 3__

**Find the HCF and LCM of these sets of numbers.**

- 30 and 39
- 20 and 40
- 12 and 36
- 42 and 64
- 32 and 72
- 12, 18 and 24
- 24, 30 and 36
- 36, 52 and 78
- 20, 40 and 60
- 100, 120 and 150

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