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Find the HCF and LCM of 26, 65… (Class 10 Maths 2023, Q27A)

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MathsCBSE Class 10 · Standard · Board exam 2023, set 30/6/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2023: question 27(A)

Set in the CBSE Class 10 board exam of 2023, paper 30/6/1, section C, question 27(A), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q27(A) · 3 marks · Short answerReal Numbers

Find the HCF and LCM of 26, 65 and 117, using prime factorisation.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/6/1.

Hints

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

Hint 1

Factorise each number. All three share one prime.

Hint 2

For the LCM, take the highest power of every prime that appears.

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. , , .

    1 mark

  2. The only prime common to all three is 13, so HCF .

    1 mark

  3. LCM .

    1 mark

Answer: HCF = 13, LCM = 1170

Where the marks are

  • Correct prime factorisation of all three numbers (1 mark)
  • HCF = 13 (1 mark)
  • LCM = 1170 (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 paper2023 board paper, set 30/6/1 (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.