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 \textbf{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: Compute LCM
\(21=3..... 7,\ 24=2^3..... 3,\ 28=2^2..... 7 \(\Rightarrow\) \text{LCM}=2^3..... 3..... 7=168.\)
Step 2: Find the first multiple in \([2000,3000]\)
\(168\times 11=1848<2000\), \(168\times 12=2016\) \(\Rightarrow\) smallest required number \(=2016\).
\[ \boxed{2016} \]