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Find the HCF and LCM of 404 and 96 and verify that product of HCF and LCM is equal to product of the two given number

Posted by Aman Tiwari 6 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 4 months ago

Prime factorisation of 404 and 96 is:

404 = 2 {tex}\times{/tex} 2 {tex}\times{/tex} 101

404 = 2² {tex}\times{/tex} 101
96 = 2 {tex}\times{/tex} 2 {tex}\times{/tex} 2 {tex}\times{/tex} 2 {tex}\times{/tex} 2 {tex}\times{/tex} 3

96 = 2⁵ {tex}\times{/tex} 3
{tex}\therefore{/tex} HCF(404,96 )= 2² = 4
LCM(404, 96 ) = 101 {tex}\times{/tex} 2⁵ {tex}\times{/tex} 3

LCM( 404, 96) = 9696

now we have to verify that,

HCF(404, 96) {tex}\times{/tex}LCM(404, 96) = 404{tex}\times{/tex}96
Hence,

LHS = HCF {tex}\times{/tex} LCM

= 4 {tex}\times{/tex} 9696

= 38784
RHS= Product of numbers

=404 {tex}\times{/tex} 96 = 38784

Since, LHS=RHS
i.e. HCF {tex}\times{/tex} LCM = Product of 404 and 96.

hence verified

0Thank You

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