Question

find LCM and HCF of 510 and 92 and verify LCM and HCF is equals to product of two numbers

Answer 1

Answer:

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Answer 2

Given: Two numbers - 510 and 92

To find: Their HCF and LCM

To verify: LCM × HCF = Product of numbers

Solution:

Calculating HCF and LCM using prime factorization method:

92 = 2 × 2 × 23 × 1

510 = 2 × 3 × 5 × 17 × 1

HCF = 2 × 1 = 2 (product of common factors)

LCM = 2 × 2 × 3 × 5 × 17 × 23 = 23460 (product of maximum frequencies of all prime factors)

Now, LCM × HCF = 23460 × 2 = 46920

and 510 × 92 = 46920

i.e. LCM × HCF = 510 × 92  = 46920 (Verified)

Hence, HCF is 2, LCM is 23460 and it has also been varified that LCM × HCF = product of two numbers.