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Find by prime factorisation… (Class 10 Maths 2023, Q26a)

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MathsCBSE Class 10 · Standard · Board exam 2023, set 30/2/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2023: question 26(a)

Set in the CBSE Class 10 board exam of 2023, paper 30/2/1, section C, question 26(a), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q26(a) · 3 marks · Short answerReal Numbers

Find by prime factorisation the LCM of the numbers and . Also, find the HCF of the two numbers.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/2/1.

Hints

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

Hint 1

Keep dividing each number by small primes; both numbers have the prime 101 as a factor.

Hint 2

LCM takes the highest power of every prime; HCF takes the lowest power of the common primes.

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. LCM = product of the highest powers of all the prime factors

    1 mark

  4. HCF = product of the lowest powers of the common prime factors

    1 mark

Answer: LCM = 90900, HCF = 1515

Where the marks are

  • Prime factorisation of 18180 (½ mark)
  • Prime factorisation of 7575 (½ mark)
  • LCM = 90900 (1 mark)
  • HCF = 1515 (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 30/2/1 (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.