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

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.