MathsCBSE Class 10 · Basic · Board exam 2024, set 430/3/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2024: question 26

Set in the CBSE Class 10 board exam of 2024, paper 430/3/1, section C, question 26, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q26 · 3 marks · Short answerReal Numbers

Find LCM and HCF of two numbers $336$ and $54$ , using prime-factorisation method.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 430/3/1.

Hints

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

Hint 1

Divide each number repeatedly by the smallest prime possible.

Hint 2

HCF uses the lowest powers of common primes; LCM uses the highest powers of all primes appearing.

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.

$336 = 2 \times 2 \times 2 \times 2 \times 3 \times 7 = 2^{4} \times 3 \times 7$
1 mark
$54 = 2 \times 3 \times 3 \times 3 = 2 \times 3^{3}$
1 mark
HCF = product of smallest powers of common prime factors $= 2 \times 3 = 6$
½ mark
LCM = product of greatest powers of all prime factors $= 2^{4} \times 3^{3} \times 7 = 16 \times 27 \times 7 = 3024$
½ mark

Answer: HCF = 6, LCM = 3024

Where the marks are

Prime factorisation $336 = 2^{4} \times 3 \times 7$ (1 mark)
Prime factorisation $54 = 2 \times 3^{3}$ (1 mark)
HCF = 6 (½ mark)
LCM = 3024 (½ 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 paper2024 board paper, set 430/3/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2024: question 26

Hints

Step-by-step solution

Revise the chapter

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