Question

If 3 is the GCD of +ve integers r, s which of the following could be GCD of 2r, 3s?
option
A. 3
B. 6
C. 9
D. 12
E. 18

Answer 1

Let r be 3m and s be 3n where m and n are +ve integers :)

Answer 2

then what..? @kc_kennylau

Answer 3

then express 2r in terms of m and 3s in terms of n

Answer 4

what is the answer?

Answer 5

@kc_kennylau

Answer 6

A

Answer 7

good responce but not clear...!

Answer 8

then don't beeping ask for the answer

Answer 9

I got an idea but it is not sutable to all GCD's

Answer 10

ans:3 suppose we take a example 6 and 27 and its gcd is 3 then we multipli by 2 and 3 to 6 and 27 the result are 12 and 81 its gcd is also 3 so

Answer 11

Let \(r=3m\) and \(s=3n\) where \(m\) and \(n\) are co-primes.
\(\therefore2r=6m\) and \(3s=9n\).
\(\because (m,n)=1\)
\(\therefore(6m,9n)=(6,9)=3\)
Where \((x,y)\) denotes the GCD of x and y

Answer 12

Tanx for your responce my dear friend...@kc_kennylau

Answer 13

no problem lol @chetan552

Answer 14

Ya i got it tanqu....@kc_kennylau

Answer 15

solution: Since 3 is GCD of r,s > 0, we can say that r = 3a, and s = 3b such that gcd(a,b) = 1 or simply a and b are relatively prime. Now, 2r = 6a, and 3s = 9b. Now, gcd(2r,3s) = gcd(6a, 9b) = 3 because gcd(a,b) = 1. So the answer is gcd(2r,3s) = 3

Answer 16

thanq u....@Lawrence1990

Answer 17

@Lawrence1990 lol your approach is the same as my approach :D

Answer 18

but my approch will gives only answer to my question
and your approch will gives answer to all questions which is similar to this....@kc_kennylau

Answer 19

i was talking to @Lawrence1990 lol

Answer 20

kk...@kc_kennylau