MathsCBSE Class 10 · Standard · Board exam 2025, set 30/3/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2025: question 23(b)

Set in the CBSE Class 10 board exam of 2025, paper 30/3/1, section B, question 23(b), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q23(b) · 2 marks · Very short answerReal Numbers

Two numbers are in the ratio $4 : 5$ and their HCF is 11. Find the LCM of these numbers.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/3/1.

Hints

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

Hint 1

Write the numbers as $4 x$ and $5 x$ . What is their HCF in terms of x?

Hint 2

Find the numbers, then use HCF × LCM = product of the two numbers.

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.

Let the numbers be $4 x$ and $5 x$ . Since 4 and 5 are co-prime, HCF $= x$ . So $x = 11$ and the numbers are 44 and 55.
½ mark
Use HCF × LCM = product of the numbers:
$LCM = \frac{44 \times 55}{11}$
1 mark
$LCM = 4 \times 55 = 220$
½ mark

Answer: LCM = 220

Where the marks are

Finds the numbers as 44 and 55 (½ mark)
Uses HCF × LCM = product of numbers (1 mark)
LCM = 220 (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 paper2025 board paper, set 30/3/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2025: question 23(b)

Hints

Step-by-step solution

Revise the chapter

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