Discussion
The product of the Least Common Factor (LCM) and Highest Common Factor (HCF) of two numbers is 24. The difference of two numbers is 2. Then the numbers are:
Answer: B
The numbers are 6 and 4.
The product of the LCM and HCF of two numbers equals the product of the numbers themselves, so the two numbers multiply to 24 and differ by 2.
\[ \begin{aligned} n(n + 2) &= 24 \\ n^2 + 2n - 24 &= 0 \\ (n + 6)(n - 4) &= 0 \end{aligned} \]
So n = 4 and the numbers are 4 and 6. Check: their HCF is 2 and their LCM is 12, and \(2 \times 12 = 24\).
The other pairs also differ by 2 but have the wrong product: 2 and 4 give 8, 8 and 6 give 48, and 8 and 10 give 80.
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