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) Input the Prime Factors into a Venn diagram 12 20 Shared Factors 12 20 3 2 6 2 10 5 2 2 2 3 2 5 3) HCF = Product of shared factors 2 × 2 = 4 12 = 2 × 2 × 3 4) LCM = Product of all factors in the diagram 2 × 2 × 3 × 5 = 60 20 = 2 × 2 × 5

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

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

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

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 2 20 = 2 × 2 × 5 2 5 3 30 = 2 × 3 × 5 3) HCF = Product of shared factors 2 × 5 = 10 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 & 24. 1) Complete Prime Factorisation for both numbers. 2) Input the Prime Factors into a Venn diagram 24 18 2 2 18 = 2 × 3 × 3 3 3 2 24 = 2 × 2 × 2 × 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

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 5 120 = 2 × 2 × 2 × 3 × 5 2 3 5 150 = 2 × 3 × 5 × 5 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

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 2 63 = 3 × 3 × 7 3 3 5 210 = 2 × 3 × 5 × 7 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

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

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

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