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Find the smallest… (Class 10 Maths Basic SQP 2025-26, Q21B)

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MathsCBSE Class 10 · Basic · Sample paper, session 2025-26 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic sample paper 2025-26: question 21(B)

From the official CBSE sample question paper for 2025-26, section B, question 21(B), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q21(B) · 2 marks · Very short answerReal Numbers

Find the smallest number which is divisible by both 306 and 657.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2025-26.

Hints

Open one hint at a time and try again before the next.

Hint 1

The smallest number that both numbers divide exactly is a well-known idea: HCF or LCM?

Hint 2

Write 306 and 657 as products of primes and take each prime with its highest power.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

  1. The smallest number divisible by both 306 and 657 is their LCM.

    ½ mark

  2. Prime factorisation: and

    1 mark

  3. LCM . So the required number is 22338.

    ½ mark

Answer: 22338

Where the marks are

  • Recognises that the required number is the LCM (½ mark)
  • Correct prime factorisations of 306 and 657 (1 mark)
  • LCM = 22338 (½ mark)

Revise the chapter

Practise this chapterBoard-style questions from Real Numbers, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2025-26 (Basic): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.