HCF LCM Prime Factorisation Demonstration This resource provides

HCF & LCM – Prime Factorisation – Demonstration This resource provides animated demonstrations of the mathematical method. Check animations and delete slides not needed for your class.

Find the Highest Common Factor (HCF) & Lowest Common Multiple (LCM) of 12 & 20. 1) Complete Prime Factorisation for both numbers. 2 3 20 12 3 2 10 6 2 Shared Factors 20 12 2 2) Input the Prime Factors into a Venn diagram 2 5 3) HCF = Product of shared factors 2× 2 12 = 2 × 3 20 = 2 × 5 =4 4) LCM = Product of all factors in the diagram 2× 2× 3× 5 = 60

Find the Highest Common Factor (HCF) & Lowest Common Multiple (LCM) of 18 & 45. 1) Complete Prime Factorisation for both numbers. 3 3 45 18 2 3 15 9 3 Shared Factors 45 18 2 2) Input the Prime Factors into a Venn diagram 3 3 5 5 3) HCF = Product of shared factors 3× 3 18 = 2 × 3 45 = 3 × 5 =9 4) LCM = Product of all factors in the diagram 2× 3× 3× 5 = 90

Find the Highest Common Factor (HCF) & Lowest Common Multiple (LCM) of 24 & 36. 1) Complete Prime Factorisation for both numbers. 36 2 12 2 18 2 6 2 2 9 3 3 Shared Factors 36 24 24 2 2) Input the Prime Factors into a Venn diagram 3 2 2 3 3) HCF = Product of shared factors 2× 2× 3 24 = 2 × 2 × 3 36 = 2 × 3 × 3 3 = 12 4) LCM = Product of all factors in the diagram 2 × 2 × 3 = 72

Find the Highest Common Factor (HCF) & Lowest Common Multiple (LCM) of 75 & 90. 1) Complete Prime Factorisation for both numbers. Shared Factors 5 2 45 3 25 5 5 90 75 5 2) Input the Prime Factors into a Venn diagram 3 9 3 3 90 = 2 × 3 × 5 5 3 3) HCF = Product of shared factors 3× 5 75 = 3 × 5 2 = 15 4) LCM = Product of all factors in the diagram 2 × 3 × 5 = 450

Find the Highest Common Factor (HCF) & Lowest Common Multiple (LCM) of 20 & 30. 1) Complete Prime Factorisation for both numbers. 2) Input the Prime Factors into a Venn diagram 30 20 20 = 2 × 5 30 = 2 × 3 × 5 2 2 5 3) HCF = Product of shared factors 2× 5 = 10 4) LCM = Product of all factors in the diagram 2× 2× 3× 5 = 60 3

Find the Highest Common Factor (HCF) & Lowest Common Multiple (LCM) of 18 & 24. 1) Complete Prime Factorisation for both numbers. 2) Input the Prime Factors into a Venn diagram 24 18 18 = 2 × 3 24 = 2 × 2 × 3 2 3 3 3) HCF = Product of shared factors 2× 3 =6 4) LCM = Product of all factors in the diagram 2× 2× 2× 3× 3 = 72 2 2

Find the Highest Common Factor (HCF) & Lowest Common Multiple (LCM) of 120 & 150. 1) Complete Prime Factorisation for both numbers. 2) Input the Prime Factors into a Venn diagram 150 120 = 2 × 2 × 3 × 5 150 = 2 × 3 × 5 2 3 2 2 3) HCF = Product of shared factors 2× 3× 5 = 30 4) LCM = Product of all factors in the diagram 2× 2× 2× 3× 5× 5 = 600 5 5

Find the Highest Common Factor (HCF) & Lowest Common Multiple (LCM) of 63 & 210. 1) Complete Prime Factorisation for both numbers. 2) Input the Prime Factors into a Venn diagram 210 63 63 = 3 × 7 210 = 2 × 3 × 5 × 7 3 3 2 7 3) HCF = Product of shared factors 3× 7 = 21 4) LCM = Product of all factors in the diagram 2× 3× 3× 5× 7 = 630 5

1) Complete Prime Factorisation for both numbers. 18 = 2 × 3 24 = 2 × 2 × 3 2) Input the Prime Factors into a Venn diagram 24 18 2 3 3) HCF = Product of shared factors 2× 3 4) LCM = Product of all factors in the diagram 2× 2× 2× 3× 3 3 2 2 =6 = 72 Find the Highest Common Factor (HCF) & Lowest Common Multiple (LCM) of these pairs of numbers. HCF = a) 20 & 30 LCM = a) 54 & 36 a) 80 & 300 b) 12 & 40 HCF = LCM = b) 80 & 24 b) 12 & 18 & 90 c) 18 & 45 HCF = LCM = c) 90 & 150 c) 80 & 150 & 180

1) Complete Prime Factorisation for both numbers. 18 = 2 × 3 24 = 2 × 2 × 3 2) Input the Prime Factors into a Venn diagram 24 18 2 3 3) HCF = Product of shared factors 2× 3 4) LCM = Product of all factors in the diagram 2× 2× 2× 3× 3 3 2 2 =6 = 72 Find the Highest Common Factor (HCF) & Lowest Common Multiple (LCM) of these pairs of numbers. HCF = 10 a) 20 & 30 LCM = 60 b) 12 & 40 HCF = 4 LCM = 120 c) 18 & 45 HCF = 9 LCM = 90 HCF = 18 a) 54 & 36 LCM = 108 a) 80 & 300 HCF = 20 LCM = 1200 b) 80 & 24 HCF = 8 LCM = 240 b) 12 & 18 & 90 c) 90 & 150 HCF = 30 LCM = 450 c) 80 & 150 & 180 HCF = 6 LCM = 180 HCF = 10 LCM = 3600

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