Skip to content

Using prime factorisation, find… (Class 10 Maths 2023, Q23)

questionbuddy.in/q/cbse-10-maths-2023-30-5-1-q23-using-prime-factorisation-hcf-lcm

MathsCBSE Class 10 · Standard · Board exam 2023, set 30/5/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2023: question 23

Set in the CBSE Class 10 board exam of 2023, paper 30/5/1, 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

Using prime factorisation, find HCF and LCM of 96 and 120.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/5/1.

Hints

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

Hint 1

Keep dividing each number by 2, then by 3, then by 5.

Hint 2

HCF takes the lowest power of each common prime; LCM takes 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. ½ mark

  2. ½ mark

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

    ½ mark

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

    ½ mark

Answer: HCF = 24, LCM = 480

Where the marks are

  • Prime factorisation 96 = 2⁵ × 3 (½ mark)
  • Prime factorisation 120 = 2³ × 3 × 5 (½ mark)
  • HCF = 24 (½ mark)
  • LCM = 480 (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 30/5/1 (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.