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Find the HCF and LCM of the numbers given below. Verify that their product is equal to the product of the given numbers: i. 32, 37 ii. 46, 51 iii. 15, 60 iv. 18, 63 v. 78, 104 |
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Answer» i. 32 = 2 x 16 = 2 x 2 x 8 = 2 x 2 x 2 x 4 = 2 x 2 x 2 x 2 x 2 x 1 37 = 37 x 1 ∴ HCF of 32 and 37 =1 LCM of 32 and 37 = 2 x 2 x 2 x 2 x 2 x 37 = 1184 HCF x LCM = 1 x 1184 = 1184 Product of the given numbers = 32 x 37 = 1184 ∴ HCF x LCM = Product of the given numbers. ii. 46 = 2 x 23 x 1 51 = 3 x 17 x 1 ∴ HCF of 46 and 51 = 1 LCM of 46 and 51 = 2 x 23 x 3 x 17 = 2346 HCF x LCM = 1 x 2346 = 2346 Product of the given numbers = 46 x 51 = 2346 ∴ HCF x LCM = Product of the given numbers iii. 15 = 3 x 5 60 = 2 x 30 = 2 x 2 x 15 = 2 x 2 x 3 x 5 ∴ HCF of 15 and 60 = 3 x 5 = 15 LCM of 15 and 60 = 3 x 5 x 2 x 2 = 60 HCF x LCM = 15 x 60 = 900 Product of the given numbers = 15 x 60 = 900 ∴ HCF x LCM = Product of the given numbers. iv. 18 = 2 x 9 = 2 x 3 x 3 63 = 3 x 21 = 3 x 3 x 7 ∴ HCF of 18 and 63 = 3 x 3 = 9 LCM of 18 and 63 = 3 x 3 x 2 x 7 = 126 HCF x LCM = 9 x 126 = 1134 Product of the given numbers = 18 x 63 = 1134 ∴ HCF x LCM = Product of the given numbers. v. 78 = 2 x 39 = 2 x 3 x 13 104 = 2 x 52 = 2 x 2 x 26 = 2 x 2 x 2 x 13 ∴ HCF of 78 and 104 = 2 x 13 = 26 LCM of 78 and 104 = 2 x 13 x 3 x 2 x 2 = 312 HCF x LCM = 26 x 312 = 8112 Product of the given numbers = 78 x 104 = 8112 ∴ HCF x LCM = Product of the given numbers. |
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