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2. Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers. (i) 26 and 91 (ii) 510 and 92 (iii) 336 and 54

2. Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers.

(i) 26 and 91

(ii) 510 and 92

(iii) 336 and 54

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 8741 Points
3 months ago
Solutions: (i) 26 and 91 Expressing 26 and 91 as product of its prime factors, we get, 26 = 2 × 13 × 1 91 = 7 × 13 × 1 Therefore, LCM (26, 91) = 2 × 7 × 13 × 1 = 182 And HCF (26, 91) = 13 Verification Now, product of 26 and 91 = 26 × 91 = 2366 And Product of LCM and HCF = 182 × 13 = 2366 Hence, LCM × HCF = product of the 26 and 91. (ii) 510 and 92 Expressing 510 and 92 as product of its prime factors, we get, 510 = 2 × 3 × 17 × 5 × 1 92 = 2 × 2 × 23 × 1 Therefore, LCM(510, 92) = 2 × 2 × 3 × 5 × 17 × 23 = 23460 And HCF (510, 92) = 2 Verification Now, product of 510 and 92 = 510 × 92 = 46920 And Product of LCM and HCF = 23460 × 2 = 46920 Hence, LCM × HCF = product of the 510 and 92. (iii) 336 and 54 Expressing 336 and 54 as product of its prime factors, we get, 336 = 2 × 2 × 2 × 2 × 7 × 3 × 1 54 = 2 × 3 × 3 × 3 × 1 Therefore, LCM(336, 54) = = 3024 And HCF(336, 54) = 2×3 = 6 Verification Now, product of 336 and 54 = 336 × 54 = 18,144 And Product of LCM and HCF = 3024 × 6 = 18,144 Hence, LCM × HCF = product of the 336 and 54.

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