1. REVIEWING HCF AND LCM ONLY FOR 3 OR 4 NUMBERS!

2. FOR 2 NUMBERS.. NOTHING CHANGES! DRAW THE VENN DIAGRAM! HCF  WHAT IS COMMON (IN THE MIDDLE) LCM  WHAT IS IN THE MIDDLE X WHAT IS LEFT IN THE OTHER TWO CIRCLES

3. 223223 2 Highest Common Factor (HCF) 24 60 5 If we multiply all the numbers in the intersection, we can quickly find the Highest Common Factor (HCF) = 2 x 2 x 3 = 12

4. 223223 2 Lowest Common Multiple (LCM) 24 60 5 If we multiply all the numbers in Venn Diagram, we get the Lowest Common Multiple (LCM) = 2 x 2 x 2 x 3 x 5 = 120

5. FOR 3 OR 4 NUMBERS… HCF – WE ALWAYS FIND WHAT IS COMMON (NOTHING CHANGES!) TO FIND THE LCM – THE METHOD WAS GIVING US A COMMON MULTIPLE, BUT NOT THE LOWEST COMMON MULTIPLE! WHY?

6. THE VENN DIAGRAM FOR 3 OR 4 NUMBERS 10 15 20 10  5,2 15  5, 3 20  5, 2, 2 5 What is common FOR 10,15 AND 20? What is common FOR 10 AND 15? 5 ONLY What is common FOR 15 AND 20 ? 5 ONLY What is common FOR 10 AND 20 ? 2 What is LEFT? 3 2 HCF = 5 LCM = 5 x 3 x 2 x 2 = 60! No. 22

7. SHORTCUT: MULTIPLY THE HIGHEST POWERS OF EACH FACTOR!! SHORTCUT TO FIND LCM (WITHOUT DRAWING VENN DIAGRAM)

8. 10  5,2 15  5, 3 20  5, 2, 2 10  5 x 2 PRIME FACTORSIN INDEX FORM 15  5 x 3 20  5 x 2 2 5x 3 x2 The HIGHEST power of EACH factor (of 5, of 3 and of 2) LCM = 5 x 3 x 2 2 = 60!!

9. THESE RULES ALSO APPLY WHEN WE HAVE 3 OR 4 NUMBERS! BOOK PG 53 EXERCISE 4J NUMBER 6: 21,42,84 7 3 76 3 7 12 3 4 2 2 7, 3 2 21 42 84 7, 3, 2 7, 2, 2, 3 What’s common? 7 and 3 HCF = 7 x 3 = 21 Times the Highest Powers of each factor (7, 3 and 2) to find the LCM LCM = 7 x 3 x 2 2 = 84 7 x 3 7 x 3 x 2 7 x 2 2 x 3

10. THESE RULES ALSO APPLY WHEN WE HAVE 3 OR 4 NUMBERS! BOOK PG 53 EXERCISE 4J NUMBER 10: 39,13,26 3 13 2 3, 13 39 13 26 13 2, 13 What’s common? 13 HCF = 13 Prime numbers don’t have prime factors, they are prime! Times the highest powers of each factor (2,3,13) LCM = 2 x 3 x 13 = 78 3 x 13 13 2 x 13

11. NUMBER 12: 10,18,20,36 10 52 5, 2 18 9 2 3 3 3, 3, 2 20 210 5 2 2, 5, 2 36 6 6 23 23 2, 3, 2, 3 What’s common? 2 HCF = 2 Times the highest powers of each factor (5,2,3) LCM =5 x 2 2 x 3 2 =180 5 x 2 3 2 x 2 2 2 x 5 2 2 x 3 2

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

13. NUMBER 20: 18,27,36 18 2 3, 3, 2 27 9 3 9 3, 3, 3 36 3, 3, 2, 2 What’s common? 3 and 3 HCF = 3 x 3 = 9 3 3 3 3 9 4 3 3 2 2 Times the highest powers of each factor (2,3) LCM = 3 3 x 2 2 = 108 3 2 x 2 3 3 2 x 2 2

14. 10  5,2 15  5, 3 20  5, 2, 2 10  5 x 2 PRIME FACTORSIN INDEX FORM 15  5 x 3 20  5 x 2 2 5x 3 x2 The HIGHEST power of EACH factor (of 5, of 3 and of 2) LCM = 5 x 3 x 2 2 = 60!! No. 22