MathsCBSE Class 10 · Standard · Board exam 2025, set 30/2/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2025: question 4

Set in the CBSE Class 10 board exam of 2025, paper 30/2/1, section A, question 4, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q4 · 1 mark · MCQReal Numbers

The least number which is a perfect square and is divisible by each of $16$ , $20$ and $50$ , is :

(A) $1200$
(B) $100$
(C) $3600$
(D) $2400$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/2/1.

Hints

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

Hint 1

Any number divisible by 16, 20 and 50 must be a multiple of their LCM.

Hint 2

Find the LCM using prime factorisation, then check whether its prime powers are all even.

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.

Factorise: $16 = 2^{4}$ , $20 = 2^{2} \times 5$ , $50 = 2 \times 5^{2}$ . So $LCM = 2^{4} \times 5^{2} = 400$ .
½ mark
$400 = 2 0^{2}$ is already a perfect square. So the least such number is $400$ , which is not among the options. Of the options, only $3600 = 6 0^{2}$ is a perfect square divisible by all three numbers, but it is not the least.
½ mark

Answer: 400 (no option is correct)

Where the marks are

Finds the LCM as 400 and notes that it is a perfect square, so no option is correct. The board gives the 1 mark for any attempt (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 paper2025 board paper, set 30/2/1 (Standard): 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.

CBSE Class 10 Mathematics Standard 2025: question 4

Hints

Step-by-step solution

Revise the chapter

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