# let a and b be two positive integers such that a p3q4 and b p2q3

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## [MCQ] Let a, b be positive integers such that a = p3 q4 and b = p^2 q

Question 1 Let a and b be two positive integers such that a = p3q4 and b = p2q3, where p and q are prime numbers. If HCF(a,b) = pmqn and LCM(a,b) = prqs , then (m + n)(r + s) = (a) 15 (b) 30 (c) 35 (d) 72Given two numbers a = p3q4 and b = p2q3Finding HCF a = p3q4 = p × p × p × q

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## Question 1 - CBSE Class 10 Sample Paper for 2023 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

Last updated at Oct. 5, 2022 by Teachoo

## Let a and b be two positive integers such that a = p 3 q 4 and b = p 2 q 3 , where p and q are prime numbers. If HCF(a,b) = p m q n and

## LCM(a,b) = p r q s , then (m + n)(r + s) =

Let a and b be two positive integers such that a = p 3 q 4 and b = p 2 q 3 , where p and q are prime numbers. If HCF(a,b) = p m q n and LCM(a,b) = p r q s , then (m + n)(r + s) = (a) 15 (b) 30 (c) 35 (d) 72

This question is similar to Question 7 - CBSE Class 10 Sample Paper for 2018 Boards

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### Transcript

Question 1 Let a and b be two positive integers such that a = p3q4 and b = p2q3, where p and q are prime numbers. If HCF(a,b) = pmqn and LCM(a,b) = prqs , then (m + n)(r + s) = (a) 15 (b) 30 (c) 35 (d) 72 Given two numbers a = p3q4 and b = p2q3 Finding HCF a = p3q4 = p × p × p × q × q × q × q b = p2q3 = p × p × q × q × q HCF = p × p × q × q × q HCF = p2q3 Comparing HCF = p2q3 with HCF = pmqn ∴ m = 2, n = 3 Finding LCM LCM = p × p × p × q × q × q × q LCM = p3q4 Comparing LCM = p3q4 with LCM = prqs ∴ r = 3, s = 4 Now, (m + n)(r + s) = (2 + 3) × (3 + 4) = 5 × 7 = 35 So, the correct answer is (c)

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## Let a and b be two positive integers such that a = p3q4 and b = p2q3, where p and q are prime numbers. If HCF (a, b) = pmqn and LCM (a, b) = prqs, then (m + n)(r + s) = ______.

Let a and b be two positive integers such that a = p3q4 and b = p2q3, where p and q are prime numbers. If HCF (a, b) = pmqn and LCM (a, b) = prqs, then (m + n)(r + s) = ______.

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Let a and b be two positive integers such that a = p3q4 and b = p2q3, where p and q are prime numbers. If HCF (a, b) = pmqn and LCM (a, b) = prqs, then (m + n)(r + s) = ______.

### OPTIONS

15 30 35 72 Advertisement Remove all ads

### SOLUTION

Let a and b be two positive integers such that a = p3q4 and b = p2q3, where p and q are prime numbers. If HCF (a, b) = pmqn and LCM (a, b) = prqs, then (m + n)(r + s) = **35**.

**Explanation:**

Given two numbers

a = p3q4 and b = p2q3

p p3q4 p p2q4 p pq4 p q4 q q3 q q2 q q 1 p p2q3 p pq3 q q3 q q2 q 1 Finding HCF

a = p3q4 = p × p × p × q × q × q × q

b = p2q3 = p × p × q × q × q

HCF = p × p × q × q × q

HCF = p2q3

Comparing HCF = p2q3 with HCF = pmqn

∴ m = 2, n = 3 p p3q4, p2q3 p p2q4, p2q3 p pq4, q3 q q4, q3 q q3, q2 q q2, q q q, 1 1, 1 Finding LCM

LCM = p × p × p × q × q × q × q

LCM = p3q4

Comparing LCM = p3q4 with LCM = prqs

∴ r = 3, s = 4

Now, (m + n)(r + s) = (2 + 3) × (3 + 4)

= 5 × 7 = 35

Concept: Fundamental Theorem of Arithmetic

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## Let a and b be two positive integers such that a = p3 q 4 and b = p2 q 3 , where p and q are prime numbers. If HCF(a,b) = pmq n and LCM(a,b) = pr q s , then (m n)(r s)=?

1. if question is asking about (m n) (r s) then, answer will be 72.2. if (m+n)(r+s) is exist there then, your answer will be 35.

Class 10 Question > Let a and b be two positive integers such tha...

Let a and b be two positive integers such that a = p3 q 4 and b = p2 q 3 , where p and q are prime numbers. If HCF(a,b) = pmq n and LCM(a,b) = pr q s , then (m n)(r s)=?

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### Answers

Aditya Raj Singh Yadav

Sep 30, 2022 Related

Let a and b be two positive integers such that a = p3 q 4 and b = p2 q 3 , where p and q are prime numbers. If HCF(a,b) = pmq n and LCM(a,b) = pr q s , then (m n)(r s)=?

1. if question is asking about (m n) (r s) then, answer will be 72.

2. if (m+n)(r+s) is exist there then, your answer will be 35.

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