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

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### Mohammed

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## If two positive integers p and q are written as p = a^2b^2 and q = a^3b , a,b are prime numbers then verify that L.C.M.(p,q) × H.C.F.(p,q) = pq

Click here👆to get an answer to your question ✍️ If two positive integers p and q are written as p = a^2b^2 and q = a^3b , a,b are prime numbers then verify that L.C.M.(p,q) × H.C.F.(p,q) = pq

Class 6 >>Maths

>>Playing With Numbers

>>Problems on HCF and LCM

>>If two positive integers p and q are wri

If two positive integers p and q are written as p=a

Question 2 b 2 and q=a 3

b, a,b are prime numbers then verify that L.C.M.(p,q)×H.C.F.(p,q)=pq

Medium Open in App Solution Verified by Toppr H.C.F.(p,q)=a 2 b L.C.M.(p,q)=a 3 b 2

L.C.M.(p,q)×H.C.F.(p,q)=a

5 b 3 pq=a 5 b 3

Therefore, L.C.M.(p,q)×H.C.F.(p,q)=pq.

283 66

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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

## 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

### 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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### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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## If two positive integers a and b are written as a = p3q2 and b = pq3; p, q are prime numbers, then HCF (a, b) is:

If two positive integers a and b are written as a = p3q2 and b = pq3; p, q are prime numbers, then HCF (a, b) is:

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If two positive integers a and b are written as a = p3q2 and b = pq3; p, q are prime numbers, then HCF (a, b) is:

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## If two positive integers a and b are written as a = p3q2 and b = pq3; p, q are prime numbers, then HCF (a, b) is:

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R Ravindra Pindel

Since a = p x p x p x q x q,

= p x q x q x q

Therefore H.C.F of a and b = pq2

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Mohammed 8 day ago

Guys, does anyone know the answer?