Question

Can two numbers have $12$ as their HCF and $512$ as their LCM? Justify your answer.

Answer 1

Let us assume that the HCF of two numbers $=12$

And LCM of two numbers $=512$

HCF is a common divisor of numbers and LCM is a common multiple of numbers, that means HCF divides both numbers perfectly and both numbers divide LCM perfectly.

HCF should also divide LCM perfectly, as it perfectly divides both numbers,

but,$\frac{512}{12}=42.667$

That means $12$ does not divide $512$ completely.

Hence, two numbers cannot have $12$ as their HCF and $512$ as LCM.