MathsCBSE Class 10 · Basic · Board exam 2023, set 430/5/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2023: question 21

Set in the CBSE Class 10 board exam of 2023, paper 430/5/1, section B, question 21, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q21 · 2 marks · Very short answerReal Numbers

Find LCM of 576 and 512 by prime factorization.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 430/5/1.

Hints

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

Hint 1

Break each number into prime factors; both are made mostly of 2s.

Hint 2

For the LCM, take every prime that appears, with the greatest power in which it 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.

Prime factorisation of 576: $576 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 = 2^{6} \times 3^{2}$
½ mark
Prime factorisation of 512: $512 = 2^{9}$
½ mark
LCM = product of the highest powers of all prime factors $= 2^{9} \times 3^{2} = 512 \times 9 = 4608$
1 mark

Answer: LCM = 4608

Where the marks are

Writes $576 = 2^{6} \times 3^{2}$ (½ mark)
Writes $512 = 2^{9}$ (½ mark)
Takes highest powers to get LCM $= 2^{9} \times 3^{2} = 4608$ (1 mark)

Revise the chapter

Chapter: Real Numbers (notes, formulas, where marks are lost and every past question)
Topic: HCF and LCM by Prime Factorisation

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 430/5/1 (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.

CBSE Class 10 Mathematics Basic 2023: question 21

Hints

Step-by-step solution

Revise the chapter

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