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

Last updated at April 16, 2024 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) =

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 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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