The L.C.M and H.C.F of two numbers are 24 and 2 respectively. Then the product…

Concept: For exactly two positive integers, the product of the numbers is always equal to the product of their LCM and their HCF — that is, a × b = LCM(a, b) × HCF(a, b). This identity does not extend directly to three or more numbers.

1. Note the given values: LCM = 24 and HCF = 2.

2. Apply the identity above: product of the two numbers = LCM × HCF.

3. Substitute the values and compute: 24 × 2 = 48.

Cross-check: A pair of numbers matching these figures is 8 and 6 — their HCF is 2 and their LCM is 24, and their product 8 × 6 also equals 48, confirming the identity.

Hence, the correct answer is 48.