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 · Board exam 2024, set 30/3/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2024: question 5

Set in the CBSE Class 10 board exam of 2024, paper 30/3/1, section A, question 5, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q5 · 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 question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/3/1.

Hints

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

Hint 1

Write 3780 as a product of primes.

Hint 2

The LCM uses the greatest power of each prime factor.

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: $3780 = 2^{2} \times 3^{3} \times 5 \times 7$ .
The LCM takes the highest power of each prime, so LCM $= 2^{2} \times 3^{x} \times 5 \times 7$ .
Comparing, $3^{x} = 3^{3}$ , so $x = 3$ , which is option (C).
1 mark

Answer: $x = 3$ , option (C)

Where the marks are

Compares prime factorisations to get $x = 3$ , option (C) (1 mark)

Revise the chapter

Chapter: Real Numbers (notes, formulas, where marks are lost and every past question)
Topic: Fundamental Theorem of Arithmetic

Practise this chapterBoard-style questions from Real Numbers, one at a time, marked against the answer key and marking points.Back to the full paper2024 board paper, set 30/3/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2024: question 5

Hints

Step-by-step solution

Revise the chapter

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