1. L.O. To be able to find the hcf AND LCM OF 3 OR 4 NUMBERS
By the end of the lesson, we will be able to:
understand that the method to find the HCF and LCM of two numbers applies to any set of numbers
choose and multiply the common prime factors to find the HCF
choose the highest power of each prime factor to find the LCM

2. Multiply The COMMON factors Only 5 is common for all three
IN INDEX FORM
PRIME FACTORS of 10, 15 and 20
10  5 x 2
10  5 x 2
15  5 x 3
15  5 x 3
20  5 x 2 x 2
20  5 x 22
Multiply The COMMON factors
Only 5 is common for all three
Multiply The HIGHEST power of EACH factor
(of 5, of 3 and of 2)
Consider the first question on the worksheet HCF and LCM of 10 and 15….let’s add 20…
HCF = 5
LCM = 5 x 3 x 22 = 60!!

3. STP 7 Pg 53 Exercise 4j: 6, 10, 11, 12, 20

4. These rules also apply when we have 3 or 4 numbers!
Multiply the Highest Powers of each factor
(2, 3 and 7) to find the LCM
LCM = 22 x 3 x 7 = 84
What’s common?
These rules also apply when we have 3 or 4 numbers!
Book Pg 53 Exercise 4j Number 6: 21,42,84
Multiply 7 and 3
HCF = 7 x 3 = 21 21 42 84 7 3 7 12 7 6
7 x 3 4 3 3 2 2 2
7 x 3 x 2
7 x 2 x 2 x 3
7 x 22 x 3

5. These rules also apply when we have 3 or 4 numbers!
Multiply the highest powers of each factor (2,3,13)
LCM = 2 x 3 x 13 = 78
What’s common?
These rules also apply when we have 3 or 4 numbers!
Book Pg 53 Exercise 4j Number 10: 39,13,26 13
HCF = 13 39 13 26
Prime numbers don’t have prime factors, they are prime! 3 13 2 13
3 x 13 13
2 x 13

6. Multiply the highest powers of each factor (2,3,5)
What’s common?
Multiply the highest powers of each factor (2,3,5)
LCM =22 x 32 x 5=180
NUMBER 11: 15,30,45,60
3 and 5
HCF = 5 x 3 = 15 15 30 45 60 15 2 15 3 15 4 3 5
3 x 5 5 3 5 3 5 3 2 2
5 x 3 x 2
5 x 3 x 3
5 x 3 x 2 x 2
5 x 32
5 x 3 x 22

7. Multiply the highest powers of each factor (2,3,5)
LCM = 22 x 32 x 5=180
What’s common?
NUMBER 12: 10,18,20,36 2
HCF = 2 10 18 20 36 5 2 9 2 2 10 6 6 3 3 2 3 2 3 5 2
5 x 2
3 x 3 x 2
2 x 5 x 2
2 x 3 x 2 x 3
32 x 2
22 x 5
22 x 32

8. Multiply the highest powers of each factor (2,3)
What’s common?
Multiply the highest powers of each factor (2,3)
LCM = 33 x 22 = 108
NUMBER 20: 18,27,36
Two 3s
HCF = 3 x 3 = 9 18 27 36 9 2 9 3 9 4 3 3 3 3 3 3 2 2
3 x 3 x 2
3 x 3 x 3
3 x 3 x 2 x 2
32 x 2 33
32 x 22

9. Have you reached this objective?
I can explain what the HCF is
I can explain what the LCM is
I can find the HCF and LCM of two numbers by listing and choosing
I can find the HCF and LCM of two numbers from the product of prime factors
I can find the HCF and LCM of more than two numbers from the product of prime factors

10. Homework
PG 53 Exercise 4j No. 18, 19 and 21