MathsCBSE Class 10 · Standard · Board exam 2023, set 30/6/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2023: question 21(B)

Set in the CBSE Class 10 board exam of 2023, paper 30/6/1, section B, question 21(B), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q21(B) · 2 marks · Very short answerReal Numbers

Find the HCF and LCM of 72 and 120.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/6/1.

Hints

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

Hint 1

Break 72 and 120 into prime factors first.

Hint 2

HCF uses the lowest powers of the common primes; LCM uses the highest powers of every prime.

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: $72 = 2^{3} \times 3^{2}$ and $120 = 2^{3} \times 3 \times 5$ .
HCF = product of the smallest powers of the common primes $= 2^{3} \times 3 = 24$ .
1 mark
LCM = product of the greatest powers of all the primes $= 2^{3} \times 3^{2} \times 5 = 360$ .
1 mark

Answer: HCF = 24, LCM = 360

Where the marks are

Correct HCF 24 from the factorisations (1 mark)
Correct LCM 360 (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 30/6/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2023: question 21(B)

Hints

Step-by-step solution

Revise the chapter

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