Is it possible that HCF and LCM of two numbers be 24 and 540 respectively? Justify the answer.

Dear Student,
HCF = 24
LCM  = 540
$Z = \frac{\mathrm{LCM}}{\mathrm{HCF}} = \frac{540}{24} = 22.5$

Since, LCM of two numbers is completely divisible by HCF of those two numbers.

Since, Here, Z= 22.5 which is not a whole number,

Hence, 540 and 24 cannot be LCM and HCF of two numbers.

Regards