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Find the greatest number less… (Class 10 Maths 2026, Q31)

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MathsCBSE Class 10 · Standard · Board exam 2026, set 30/4/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2026: question 31

Set in the CBSE Class 10 board exam of 2026, paper 30/4/1, section C, question 31, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q31 · 3 marks · Short answerReal Numbers

Find the greatest number less than 10,000 which is exactly divisible by 48, 60 and 65.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/4/1.

Hints

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

Hint 1

A number divisible by 48, 60 and 65 must be a multiple of their LCM.

Hint 2

Find the LCM, then find its largest multiple that is still less than 10,000.

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: , , .

    1½ marks

  2. LCM.

    1 mark

  3. Any number divisible by all three is a multiple of 3120: , but . So the required number is .

    ½ mark

Answer: 9360

Where the marks are

  • Correct prime factorisation of 48, 60 and 65 (1½ marks)
  • LCM = 3120 (1 mark)
  • Greatest multiple below 10,000 = 9360 (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 paper2026 board paper, set 30/4/1 (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.