HCF & LCM – Prime Factorisation – Worksheet A Worksheets increase in difficulty and are in 2 sizes

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EXAMPLE 1) Find the Highest Common Factor (HCF) & Lowest Common Multiple (LCM) of 18 and 42. a) Start by finding the Prime Factors of each number. 18 9 2 3 42 21 2 3 7 : 2×3×3 18 : 2×3×7 42 b) Complete a Venn diagram with the factors. 18 42 2 Factors both numbers share. 3 7 18 42 2 3 3 2 3 7 c) The HCF is the product of the shared factors. HCF = 2 × 3 = 6 d) The LCM is the product of all the factors in the Venn diagram. LCM = 3 × 2 × 3 × 7 = 126

① Finding HCF & LCM Using Prime Factorisation 3) Find the HCF & LCM of 60 & 75. 60 75 EXAMPLE 1) Find the Highest Common Factor (HCF) & Lowest Common Multiple (LCM) of 18 and 42. a) Find the Prime Factors. 60 : 75 : a) Start by finding the Prime Factors of each number. 18 9 2 3 42 21 2 3 7 b) Complete the Venn Diagram. : 2×3×3 18 : 2×3×7 42 60 75 c) HCF = b) Complete a Venn diagram with the factors. 18 42 2 Factors both numbers share. 3 7 d) LCM = 18 42 2 3 3 2 3 7 4) Find the HCF & LCM of 90 & 120. a) Find the Prime Factors. c) The HCF is the product of the shared factors. 90 : 120 : HCF = 2 × 3 = 6 d) The LCM is the product of all the factors in the Venn diagram. LCM = 3 × 2 × 3 × 7 = 126 b) Complete the Venn Diagram. 2) Find the Highest Common Factor (HCF) & Lowest Common Multiple (LCM) of 12 and 42. c) HCF = d) LCM = a) Find the Prime Factors. 12 42 5) Find the HCF & LCM of 84 & 140. 18 : 42 : a) Find the Prime Factors. 84 : 140 : b) Complete the Venn Diagram. c) HCF = multiply shared factors 12 42 Factors both numbers share. HCF = b) Complete a Venn Diagram. d) LCM = multiply all the diagram factors c) HCF = LCM = d) LCM =

HCF = 15 LCM = 300 HCF = 30 LCM = 360 HCF = 6 LCM = 84 HCF = 28 ① Finding HCF & LCM Using Prime Factorisation 3) Find the HCF & LCM of 60 & 75. 60 75 2 30 3 25 EXAMPLE 1) Find the Highest Common Factor (HCF) & Lowest Common Multiple (LCM) of 18 and 42. a) Find the Prime Factors. 2 15 HCF = 15 LCM = 300 5 5 60 : 2×2×3×5 75 : 3×5×5 a) Start by finding the Prime Factors of each number. 18 9 2 3 42 21 2 3 7 3 5 b) Complete the Venn Diagram. : 2×3×3 18 : 2×3×7 42 60 75 c) HCF = 3 × 5 = 15 2 3 5 b) Complete a Venn diagram with the factors. 18 42 2 Factors both numbers share. 3 7 5 2 d) LCM = 2 × 2 × 3 × 5 × 5 = 300 18 42 2 3 3 2 3 7 4) Find the HCF & LCM of 90 & 120. 90 120 2 45 2 60 a) Find the Prime Factors. c) The HCF is the product of the shared factors. 3 15 2 30 90 : 2×3×3×5 120 : 2×2×2×3×5 HCF = 2 × 3 = 6 HCF = 30 LCM = 360 3 5 2 15 d) The LCM is the product of all the factors in the Venn diagram. 3 5 LCM = 3 × 2 × 3 × 7 = 126 b) Complete the Venn Diagram. 90 120 2) Find the Highest Common Factor (HCF) & Lowest Common Multiple (LCM) of 12 and 42. c) HCF = 2 × 3 × 5 = 30 2 3 2 3 5 d) LCM = 3 × 3 × 2 × 5 × 2 × 2 = 360 2 a) Find the Prime Factors. 12 6 2 3 42 21 2 3 7 5) Find the HCF & LCM of 84 & 140. 84 140 : 2×2×3 : 22×3 12 : 2×3×7 42 HCF = 6 LCM = 84 2 42 2 70 a) Find the Prime Factors. 2 21 HCF = 28 LCM = 420 2 84 : 2×2×3×7 140 : 2×2×5×7 35 b) Complete the Venn Diagram. 3 7 5 7 c) HCF = multiply shared factors 12 42 2 Factors both numbers share. 3 7 HCF = 2 × 3 = 6 b) Complete a Venn Diagram. 84 140 d) LCM = multiply all the diagram factors c) HCF = 2 × 2 × 7 = 28 3 2 2 7 5 LCM = 2 × 2 × 3 × 7 = 84 d) LCM = 3 × 2 × 2 × 7 × 5 = 420

HCF = 45 LCM = 540 HCF = 35 LCM = 1050 HCF = 72 LCM = 864 HCF = 20 ② Finding HCF & LCM Using Prime Factorisation 4) Find the HCF & LCM of 180 & 135. HCF = 45 LCM = 540 EXAMPLE 1) Find the Highest Common Factor (HCF) & Lowest Common Multiple (LCM) of 18 and 42. 108 135 a) Start by finding the Prime Factors of each number. 18 9 2 3 42 21 2 3 7 HCF = 3 × 3 × 5 = 45 2 3 3 3 2 5 : 2×3×3 18 : 2×3×7 42 LCM = 2 × 2 × 3 × 3 × 3 × 5 = 540 5) Find the HCF & LCM of 210 & 175. b) Complete a Venn diagram with the factors. 18 42 2 Factors both numbers share. 3 7 18 42 HCF = 35 LCM = 1050 2 3 3 2 3 7 c) The HCF is the product of the shared factors. HCF = 2 × 3 = 6 HCF = 7 × 5 = 35 LCM = 2 × 3 × 5 × 5 × 7 = 1050 d) The LCM is the product of all the factors in the Venn diagram. 6) Find the HCF & LCM of 288 & 216. LCM = 3 × 2 × 3 × 7 = 126 288 216 2) Find the HCF & LCM of 100 & 60. 100 60 HCF = 72 LCM = 864 2 2 2 3 2 3 HCF = 20 LCM = 300 a) Find the Prime Factors. 2 3 b) Complete the Venn Diagram. 100 60 HCF = 23 × 32 = 72 LCM = 25 × 33 = 864 c) HCF = 2 × 2 × 5 = 20 2 162 5 3 7) Find the HCF & LCM of 108, 162 & 135. 2 5 108 d) LCM = 2 × 2 × 3 × 5 × 6 = 300 2 2 3) Find the HCF & LCM of 72 & 108. 3 HCF = 36 LCM = 216 HCF = 27 LCM = 1620 3 3 a) Find the Prime Factors. 3 b) Complete the Venn Diagram. 72 108 135 c) HCF = 2 × 2 × 3 × 3 = 36 5 3 2 3 3 2 d) LCM = 2 × 2 × 2 × 3 × 3 × 3 = 216 2 HCF = 33 = 27 LCM = 22 × 34 × 5 = 1620

A = 135 B = 900 90 & 54 HCF = 30 LCM = 450 HCF = 45 HCF = 70 ③ Finding HCF & LCM Using Prime Factorisation 5) The LCM of these two numbers is 2700. What are the two numbers? A B 1) Find the HCF & LCM of 90 & 150. 5 A = 135 B = 900 3 3 A = 135 a) Find the Prime Factors. 3 5 2 2 B = 900 b) Complete the Venn Diagram. 90 150 6) For two numbers both less than 100, the HCF is 18 and the LCM is 270. What are the two numbers? c) HCF = the product of the shared factors. HCF = 2 × 3 × 5 = 30 90 & 54 HCF = 30 LCM = 450 d) LCM = the product of all the factors in the Venn diagram. LCM = 22 × 33 × 53 = 450 7) Find the HCF & LCM of 135, 270 & 225. 135 270 2) Find the HCF & LCM of 350 & 280. 3 350 280 HCF = 45 LCM = 1350 2 HCF = 70 LCM = 1400 3 3 5 225 5 HCF = 2 × 5 × 7 = 70 LCM = 23 × 52 × 7 = 1400 3) Find the HCF & LCM of 288 & 120. HCF = 32 × 5 = 45 LCM = 2 × 33 × 52 = 1350 3 must be here 8) The HCF of A, B, & C is 6. The HCF of A & B is 36. The HCF of B & C is 42. The HCF of A & C is 30. B = 252 The LCM of A, B & C is 18900. Complete the Venn Diagram. What numbers are A & C? HCF = 24 LCM = 1440 A B C 3 3 2 HCF = 23 × 3 = 24 LCM = 25 × 32 × 5 = 1440 2 4) The HCF of A and B is 28. What are A and B? 3 5 7 A = 392 B = 84 A B A = 540 C = 1050 7 A = 392 5 2 7 3 A = 540 2 2 B = 84 C = 1050

① Finding HCF & LCM Using Prime Factorisation 3) Find the HCF & LCM of 60 & 75. 60 75 EXAMPLE 1) Find the Highest Common Factor (HCF) & Lowest Common Multiple (LCM) of 18 and 42. a) Find the Prime Factors. 60 : 75 : a) Start by finding the Prime Factors of each number. 18 9 2 3 42 21 2 3 7 b) Complete the Venn Diagram. : 2×3×3 18 : 2×3×7 42 60 75 c) HCF = b) Complete a Venn diagram with the factors. 18 42 2 Factors both numbers share. 3 7 d) LCM = 18 42 2 3 3 2 3 7 4) Find the HCF & LCM of 90 & 120. a) Find the Prime Factors. c) The HCF is the product of the shared factors. 90 : 120 : HCF = 2 × 3 = 6 d) The LCM is the product of all the factors in the Venn diagram. LCM = 3 × 2 × 3 × 7 = 126 b) Complete the Venn Diagram. 2) Find the Highest Common Factor (HCF) & Lowest Common Multiple (LCM) of 12 and 42. c) HCF = d) LCM = a) Find the Prime Factors. 12 42 5) Find the HCF & LCM of 84 & 140. 18 : 42 : a) Find the Prime Factors. 84 : 140 : b) Complete the Venn Diagram. c) HCF = multiply shared factors 12 42 Factors both numbers share. HCF = b) Complete a Venn Diagram. d) LCM = multiply all the diagram factors c) HCF = LCM = d) LCM =

② Finding HCF & LCM Using Prime Factorisation 4) Find the HCF & LCM of 180 & 135. EXAMPLE 1) Find the Highest Common Factor (HCF) & Lowest Common Multiple (LCM) of 18 and 42. a) Start by finding the Prime Factors of each number. 18 9 2 3 42 21 2 3 7 HCF : 2×3×3 18 : 2×3×7 42 LCM = 5) Find the HCF & LCM of 210 & 175. b) Complete a Venn diagram with the factors. 18 42 2 Factors both numbers share. 3 7 18 42 2 3 3 2 3 7 c) The HCF is the product of the shared factors. HCF = 2 × 3 = 6 HCF = LCM = d) The LCM is the product of all the factors in the Venn diagram. 6) Find the HCF & LCM of 288 & 216. LCM = 3 × 2 × 3 × 7 = 126 2) Find the HCF & LCM of 100 & 60. 100 60 a) Find the Prime Factors. b) Complete the Venn Diagram. 100 60 HCF = LCM = c) HCF = 7) Find the HCF & LCM of 108, 162 & 135. d) LCM = 3) Find the HCF & LCM of 72 & 108. a) Find the Prime Factors. b) Complete the Venn Diagram. 72 108 c) HCF = d) LCM = HCF = LCM =

③ A B C Finding HCF & LCM Using Prime Factorisation 5) The LCM of these two numbers is 2700. What are the two numbers? A B 1) Find the HCF & LCM of 90 & 150. 5 3 A = 2 a) Find the Prime Factors. 2 B = b) Complete the Venn Diagram. 90 150 6) For two numbers both less than 100, the HCF is 18 and the LCM is 270. What are the two numbers? c) HCF = the product of the shared factors. HCF = d) LCM = the product of all the factors in the Venn diagram. LCM = 7) Find the HCF & LCM of 135, 270 & 225. 2) Find the HCF & LCM of 350 & 280. 350 280 HCF = LCM = 3) Find the HCF & LCM of 288 & 120. HCF = LCM = 8) The HCF of A, B, & C is 6. The HCF of A & B is 36. The HCF of B & C is 42. The HCF of A & C is 30. B = 252 The LCM of A, B & C is 18900. Complete the Venn Diagram. What numbers are A & C? A B C HCF = LCM = 4) The HCF of A and B is 28. What are A and B? A B 7 A = 3 A = 2 B = C =

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