For two positive integers a and b, the product a × b equals HCF(a, b) × LCM(a, b). Here, one number is 24, the HCF is 6 and the LCM is 72. Let the other number be n. Then 24 × n = 6 × 72. The right-hand side is 432, so n = 432 ÷ 24 = 18. Hence, the other number must be 18 to maintain both the given HCF and LCM.
Option A:
Option A, 12, would give 24 × 12 = 288, and since 6 × 72 = 432, the product condition would fail. It also changes the LCM and HCF relationship.
Option B:
Option B satisfies 24 × 18 = 432, matching 6 × 72 exactly. It ensures the pair of numbers has the stated HCF and LCM by the standard product relation.
Option C:
Option C, 36, gives a product of 864, which would require a different LCM or HCF than those given.
Option D:
Option D, 48, yields an even larger product and is inconsistent with the specified values of 6 and 72.
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