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.
Unit 8 Lesson 7: Exercise 2
Find the LCM of the following sets of numbers using any method.
Unit 8 Lesson 9: Exercise 3
Find the HCF and LCM of these sets of numbers.