Question

can two no. have 16 their HCF & 324 as their LCM? give reason?

Answer 1

HCF- highest common factor

for two number, their HCF is the largest number which divides both.

LCM- least common multiple

for two number their LCM is the smallest number which is a multiple of both.

now HCF divides both numbers, and both numbers perfectly divides LCM.

so, HCF must perfectly divides LCM.

in other words, for LCM÷HCF remainder must be zero

here, LCM=324
and,HCF=16

clearly, 324/16
=20.25 (remainder is not zero)

thus, there do not exist two number whose HCF is 16 and LCM is 324.

I HOPE THIS HELPS YOU!