Question

Find the LCM and HCF of 510 and 92 and verify that LCM.HCF = product of the two numbers. [4 MARKS]

Answer 1

Prime factorisation : 1 Mark
H.C.F : 1 Mark
L.C.M : 1 Mark
Verification : 1 Mark


For 510 and 92

$510=2\times 3\times 5\times 17$

$92=2\times 2\times 23=2^2\times 23$

HCF = Product of the smallest power of each common prime factor in the numbers = 2

LCM = Product of the greatest power of each prime factor involved in the numbers
= $2^2\times 3\times 5\times 17\times 23=23460$

$LCM\times HCF=2\times 23460=46920$

Product of two given numbers
$=510\times 92=46920$

Therefore, it is proved that LCM $\times$ HCF = product of two given numbers.