Question

Is it possible that HCF and LCM of two numbers is 24 and 540 respectively . Justify your answer.

Answer 1

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 example1200 = 2⁴ + 3¹ + 5² = 2 × 2 × 2 × 2 × 3 × 5 × 5This theorem is stating two things. First that 1200 can be represented as a product of prime numbers, and second , no matter how this is done, there will always be four 2s and one 3 and two 5s and no other primes in the product. The requirement that the factors be prime is necessary.It is not possible in this question that H.C.F and L.C.M of 2 numbers be 24 and 540 respectively because the H.C.F. is always suppose to be the factor of L.C.M. Here if we divide 540 by 24 we will get 12 as remainder, it means that 24 is not a factor of 540 or here, H.C.F. is not a factor of L.C.M.

Answer 2

Answer:

No, since 24 is not a factor of 540