HCF and LCM properties – UGC NET Question

Statement A gives the fundamental relationship between HCF, LCM and the product of two positive integers. Statement C correctly defines LCM as the least positive common multiple. Statement D is also true; co-prime numbers have no common positive factor other than 1. Statement B is false because the HCF cannot exceed the numbers themselves, and E is false since if one number divides the other, the HCF is the smaller number, not necessarily 1. Thus, A, C and D only are correct, matching option A.

Option A:
Option A is correct because it combines the key algebraic relation with the proper descriptions of LCM and co-primality, while excluding B and E, which misunderstand bounds on HCF and the divisor case.

Option B:
Option B is incomplete as it includes only A and C and omits D, thereby failing to highlight the link between co-prime numbers and HCF, which is frequently tested.

Option C:
Option C is incorrect because it drops A and includes only C and D, so it loses the important multiplicative connection between HCF and LCM and provides an incomplete set of correct statements.

Option D:
Option D is wrong since it includes B, which wrongly claims that the HCF is at least as large as each number, contradicting basic number theory, and therefore the combination cannot be accepted.