HCF and LCM key properties – UGC NET Question

Statements A, C and D correctly summarise key properties of HCF and LCM. A gives the fundamental relationship a × b = HCF(a, b) × LCM(a, b) for positive integers. C is true because the LCM is defined as the least common multiple of the numbers. D is correct since when one number divides the other, the smaller is their HCF and the larger is their LCM. B is false because the HCF cannot exceed the smaller number, and E is false because distinct primes have HCF equal to 1, not one of them, so A, C and D only are correct.

Option A:
Option A is incomplete because it omits D, failing to mention the simple special case where one number divides the other, which is frequently used in problems. Even though it includes two true statements, it does not list all of them.

Option B:
Option B is correct as it gathers all the true properties given, including the product relationship, the multiple property of LCM and the special divisor case, while excluding the incorrect descriptions in B and E.

Option C:
Option C is wrong because it includes E, which misstates the HCF of distinct prime numbers. By adding this false statement, it makes the combination invalid.

Option D:
Option D is incomplete since it leaves out A, the central product formula linking HCF and LCM, so it does not provide the full set of correct statements among those listed.