If a = 2² × 3^x, b = 2² × 3 × 5, c = 2² × 3 × 7 and LCM (a,b,c) = 3780, then x is equal to (A) 1 (B) 2 (C) 3 (D) 0

MathsCBSE Class 10 · Standard · Sample paper, session 2025-26 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard sample paper 2025-26: question 1

From the official CBSE sample question paper for 2025-26, section A, question 1, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q1 · 1 mark · MCQReal Numbers

If $a = 2^{2} \times 3^{x}$ , $b = 2^{2} \times 3 \times 5$ , $c = 2^{2} \times 3 \times 7$ and LCM $(a, b, c) = 3780$ , then $x$ is equal to

(A)1
(B)2
(C)3
(D)0

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2025-26.

Hints

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

Hint 1

The LCM uses the highest power of each prime that appears in a, b and c.

Hint 2

Write the LCM as $2^{2} \times 3^{x} \times 5 \times 7$ and set it equal to 3780.

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.

The LCM takes the highest power of each prime. Assuming $x \geq 1$ : LCM $(a, b, c) = 2^{2} \times 3^{x} \times 5 \times 7 = 140 \times 3^{x}$
Set $140 \times 3^{x} = 3780$ . Then $3^{x} = \frac{3780}{140} = 27 = 3^{3}$ , so $x = 3$ .
1 mark
Hence the answer is option (C).

Answer: x = 3, option (C)

Where the marks are

Writes the LCM as $140 \times 3^{x}$ , equates it to 3780 and gets $x = 3$ , option (C) (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 paperSample paper 2025-26 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard sample paper 2025-26: question 1

Hints

Step-by-step solution

Revise the chapter

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