If two positive integers p and q can be expressed as p=18a²b^4 and q=20a³b², where a and b are prime numbers, then LCM (p,q) is: (A) 2a²b² (B) 180a²b² (C) 12a²b² (D) 180a³b^4

MathsCBSE Class 10 · Standard · Board exam 2024, set 30/1/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2024: question 5

Set in the CBSE Class 10 board exam of 2024, paper 30/1/1, 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 two positive integers $p$ and $q$ can be expressed as $p = 18 a^{2} b^{4}$ and $q = 20 a^{3} b^{2}$ , where $a$ and $b$ are prime numbers, then LCM $(p, q)$ is:

(A) $2 a^{2} b^{2}$
(B) $180 a^{2} b^{2}$
(C) $12 a^{2} b^{2}$
(D) $180 a^{3} b^{4}$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/1/1.

Hints

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

Hint 1

Factorise 18 and 20 into primes first.

Hint 2

The LCM takes 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.

Write the prime factorisations: $p = 2 \times 3^{2} \times a^{2} b^{4}$ and $q = 2^{2} \times 5 \times a^{3} b^{2}$ .
The LCM is the product of the highest powers: $2^{2} \times 3^{2} \times 5 \times a^{3} b^{4} = 180 a^{3} b^{4}$ . The answer is option (D).
1 mark

Answer: $180 a^{3} b^{4}$ , option (D)

Where the marks are

Takes the highest powers of all prime factors to get $180 a^{3} b^{4}$ , option (D) (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 paper2024 board paper, set 30/1/1 (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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