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)
Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.
Hi, it looks like you're using AdBlock :(
Displaying ads are our only source of revenue. To help Teachoo create more content, and view the ad-free version of Teachooo... please purchase Teachoo Black subscription.
Please login to view more pages. It's free :)
Teachoo gives you a better experience when you're logged in. Please login :)
Solve all your doubts with Teachoo Black!
Teachoo answers all your questions if you are a Black user!