State fundamental theorem of arithmetic. Is it possible that H.C.F and L.C.M of 2 numbers be 24 and 540 respectively? Justify your Answer.

Fundamental Theorem of Arithmetic:-

In number theory, the fundamental theorem of arithmetic also called the unique factorization theorem or the unique prime factorization theorem states that every integer greater than 1 either is prime itself or is the product of prime numbers and that this product is unique, up to the order of factors. For example

It is not possible as asked in the question that H.C.F and L.C.M of 2 numbers were 24 and 540 respectively because the H.C.F. is always a factor of L.C.M.

Here,

If we divide 540 by 24 we will get 12 as a remainder,

That means that 24 is not a factor of 540.

Or here in this question, H.C.F. is not a factor of L.C.M.