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Assertion (A): For any… (Class 10 Maths Basic 2025, Q19)

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MathsCBSE Class 10 · Basic · Board exam 2025, set 430/1/1 · 1 mark · Assertion-reason

CBSE Class 10 Mathematics Basic 2025: question 19

Set in the CBSE Class 10 board exam of 2025, paper 430/1/1, section A, question 19, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q19 · 1 mark · Assertion-reasonCompetency-basedReal Numbers

Assertion (A): For any two natural numbers a and b, the HCF of a and b is a factor of the LCM of a and b.

Reason (R): HCF of any two natural numbers divides both the numbers.

Codes: (A) Both A and R are true and R is the correct explanation of A. (B) Both A and R are true, but R is not the correct explanation of A. (C) A is true, but R is false. (D) A is false, but R is true.

  1. (A)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  2. (B)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
  3. (C)Assertion (A) is true, but Reason (R) is false.
  4. (D)Assertion (A) is false, but Reason (R) is true.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/1/1.

Hints

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

Hint 1

Does the HCF divide ?

Hint 2

Does divide the LCM?

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.

  1. R is true: the HCF divides both and .

  2. Since the HCF divides , and divides the LCM, the HCF divides the LCM. So A is true, and R is the correct explanation of A. The answer is option (A).

    1 mark

Answer: Option (A)

Where the marks are

  • Both statements true and R explains A (1 mark)

Revise the chapter

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 430/1/1 (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.