Statements A and B define HCF and LCM correctly, D notes that prime factorisation is a standard method to compute them and E highlights their application to repeated event and synchronisation problems, all of which are true. Statement C is false because in general a × b = HCF(a, b) × LCM(a, b), not just HCF(a, b). Therefore, the combination A, B, D and E only is the set of correct statements.
Option A:
Option A is incomplete as it omits E and thus fails to mention how HCF and LCM play a role in real exam problems involving repeated cycles and meeting times. Without E, the practical context of these concepts is under-emphasised.
Option B:
Option B is correct since it includes all the true statements and rightly excludes C, which confuses the relationship between product, HCF and LCM. It reflects both the definitions and the application of these notions in aptitude questions.
Option C:
Option C is wrong because it contains C, the incorrect equality, even though it also includes some true statements. The presence of C makes the overall combination mathematically inaccurate.
Option D:
Option D is incorrect as it includes C and omits B, thereby endorsing a false formula while ignoring the correct definition of LCM as the smallest common multiple. This mixture cannot be accepted as correct.
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