Skip to content

Find the LCM and HCF of… (Class 10 Maths Basic 2023, Q23)

questionbuddy.in/q/cbse-10-maths-2023-430-1-1-q23-lcm-hcf-using-prime-factorisation

MathsCBSE Class 10 · Basic · Board exam 2023, set 430/1/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2023: question 23

Set in the CBSE Class 10 board exam of 2023, paper 430/1/1, section B, question 23, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q23 · 2 marks · Very short answerReal Numbers

Find the LCM and HCF of 92 and 510, using prime factorisation.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 430/1/1.

Hints

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

Hint 1

Break each number into prime factors by repeated division.

Hint 2

HCF uses only common primes with lowest powers; LCM uses every prime with 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. ½ mark

  2. ½ mark

  3. HCF = product of smallest powers of common prime factors

    ½ mark

  4. LCM = product of greatest powers of all prime factors

    ½ mark

Answer: HCF = 2, LCM = 23460

Where the marks are

  • Prime factorisation of 92 (½ mark)
  • Prime factorisation of 510 (½ mark)
  • HCF = 2 (½ mark)
  • LCM = 23460 (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 paper2023 board paper, set 430/1/1 (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.