Question

Find the HCF and LCM of 404 and 96 and verify that HCFxLCM=Product of two given numbers.

Answer 1

Q. Find the HCF and LCM of 404 and 96 and verify that HCF×LCM = product of two given numbers.

Solution :

First do the prime factorisation of 404 and 96 ,

96 = 2×2×2×2×2×3 = (2)^5

404 = 2×2×101 = (2)^2

Therefore, HCF of 404 and 96 is (2)^2 = 4

Now,

LCM (404,96) = (404×96)/HCF

= (404×96)/4 = 9696

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Verification :

⭐ HCF×LCM = product of two given numbers.

HCF = 4
LCM = 9696
Product of 96,404 = 96×404 = 38784

Product of HCF and LCM
= 4×9696 = 38784

Hence,
HCF×LCM = product of two given numbers. (verified)