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

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!!

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

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

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

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

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

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

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

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