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State the 'Fundamental… (Class 10 Maths Basic 2025, Q26b)

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MathsCBSE Class 10 · Basic · Board exam 2025, set 430/2/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2025: question 26(b)

Set in the CBSE Class 10 board exam of 2025, paper 430/2/1, section C, question 26(b), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q26(b) · 3 marks · Short answerReal Numbers

State the 'Fundamental Theorem of Arithmetic' and use it to find LCM of 36 and 54.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/2/1.

Hints

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

Hint 1

The theorem is about writing composite numbers as products of primes — and uniqueness.

Hint 2

Factorise 36 and 54 into primes using exponents.

Hint 3

For LCM, take each prime with its 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. Fundamental Theorem of Arithmetic: Every composite number can be expressed (factorised) as a product of primes, and this factorisation is unique apart from the order in which the prime factors occur.

    1 mark

  2. .

    ½ mark

  3. .

    ½ mark

  4. LCM = product of the greatest power of each prime factor .

    1 mark

Answer: LCM(36, 54) = 2²×3³ = 108

Where the marks are

  • Correct statement of FTA (1 mark)
  • Prime factorisation of 36 (½ mark)
  • Prime factorisation of 54 (½ mark)
  • LCM = 108 (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 paper2025 board paper, set 430/2/1 (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.