Question

Find the smallest number between 2000 and 3000 that is exactly divisible by 21, 24 and 28.

• A. None of these
• B. 2000
• C. 2352
• D. 2016

Hint:

For “exactly divisible by several numbers,” take the LCM} and scan multiples within the interval. Multiplying once more than the floor of \(\frac{\text{lower bound}}{\text{LCM}}\) gives the first valid multiple.

Answer 1

The Correct Option is D

Step 1: Calculate LCM
\(21 = 3 \times 7,\; 24 = 2^3 \times 3,\; 28 = 2^2 \times 7 \;\Rightarrow\; \text{LCM} = 2^3 \times 3 \times 7 = 168.\)

Step 2: Determine the first multiple within [2000,3000]
\(168 \times 11 = 1848 < 2000,\; 168 \times 12 = 2016 \;\Rightarrow\; \text{smallest required number} = 2016.\)

\[\boxed{2016}\]