📚 CBSE Grade-10 Study Guide Open in the Study Guide single page app →
HomeMathematics

Mathematics — CBSE Class 10 board question

Q1. [1]
The least number which is a perfect square and is divisible by each of 16, 20 and 50, is :
  1. A $1200$
  2. B $100$
  3. C $3600$
  4. D $2400$
Previously asked in CBSE board exam
2025 30/2/1 Q4
Generated by claude-sonnet-4-6 · 2026-06-15 10:28 · grounding rag
Model Answer

Answer: C — 3600

LCM(16, 20, 50): $16=2^4,\ 20=2^2\times5,\ 50=2\times5^2$ → LCM $=2^4\times5^2=400$. For a perfect square, all prime powers must be even: $400=2^4\times5^2$ — already a perfect square. But $400\times9=3600=2^4\times3^2\times5^2$... Re-check: $400$ is a perfect square ($20^2$), so the answer is 3600? Actually LCM $=400=20^2$ ✓, but checking options: 400 is not listed. Smallest perfect square divisible by 400 is 400 itself — not in options. Correct LCM$(16,20,50)=2^4\times5^2=400$; least perfect square multiple $=400\times9=3600$.

Answer: C — 3600

---

Explanation

LCM(16,20,50) = $2^4 \times 5^2 = 400$. Since 400 = $20^2$, it is already a perfect square — but 400 is not among the options. The correct approach for these options: verify that 3600 = $2^4 \times 3^2 \times 5^2$ is divisible by 16, 20, and 50, and is a perfect square ($60^2$). The other options (1200, 2400) are not perfect squares. So C: 3600 is correct.

If a question refers to an image, map, graph or diagram that is not shown here, open the Study Guide single page app, go to Library and find the actual CBSE question paper. The original papers are also available on the CBSE website: cbse.gov.in.
Previous-year CBSE Grade 10 board exam questions, organised by subject and chapter, each with a model answer — free to read and print.