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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. Q.2

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How can i easily solve the HCF and LCM. This is the best question of class 10th maths. I want to know the answer of this question please give me best solution of this question 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.

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  1. (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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