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Find the smallest number which… (Class 10 Maths 2025, Q23a)

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MathsCBSE Class 10 · Standard · Board exam 2025, set 30/3/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2025: question 23(a)

Set in the CBSE Class 10 board exam of 2025, paper 30/3/1, section B, question 23(a), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q23(a) · 2 marks · Very short answerReal Numbers

Find the smallest number which is divisible by both 644 and 462.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/3/1.

Hints

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

Hint 1

The smallest number divisible by two numbers is their LCM.

Hint 2

Factorise both numbers into primes. Then 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. Prime factorisation:

    ½ mark

  2. ½ mark

  3. The smallest number divisible by both is their LCM. Take each prime factor with its highest power:

    So the required smallest number is 21252.

    1 mark

Answer: 21252

Where the marks are

  • Prime factorisation of 462 (½ mark)
  • Prime factorisation of 644 (½ mark)
  • LCM = 21252 identified as the required number (1 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 paper2025 board paper, set 30/3/1 (Standard): 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.