MathsCBSE Class 10 · Basic · Board exam 2026, set 430/5/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2026: question 22

Set in the CBSE Class 10 board exam of 2026, paper 430/5/1, section B, question 22, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q22 · 2 marks · Very short answerReal Numbers

Find the H.C.F. and L.C.M. of 1530 and 2040.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 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 by repeated division.

Hint 2

HCF uses the lowest power of each common prime; LCM uses the highest power of every prime present.

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.

$1530 = 2 \times 3^{2} \times 5 \times 17$
½ mark
$2040 = 2^{3} \times 3 \times 5 \times 17$
½ mark
HCF = product of smallest powers of common primes $= 2 \times 3 \times 5 \times 17 = 510$
½ mark
LCM = product of greatest powers of all primes $= 2^{3} \times 3^{2} \times 5 \times 17 = 6120$
½ mark

Answer: HCF = 510, LCM = 6120

Where the marks are

Prime factorisation of 1530 (½ mark)
Prime factorisation of 2040 (½ mark)
HCF = 510 (½ mark)
LCM = 6120 (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 paper2026 board paper, set 430/5/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2026: question 22

Hints

Step-by-step solution

Revise the chapter

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