Question

Aisha, Benoit, and Carleen are each thinking of a positive integer.
Aisha's number and Benoit's number have a common divisor greater than 1.
Aisha's number and Carleen's number also have a common divisor greater than 1.
Benoit's number and Carleen's number also have a common divisor greater than 1.
Is it necessarily true that the greatest common divisor of all three numbers is greater than 1?
If it is necessarily true, explain how you know it's true.If it isn't necessarily true, convince me by showing me three numbers for which it's false.

Answer 1

Hmmm, i don't want to directly give you the answer so let me tell you this. I have numbers A, B and C such that hcf(A,B)=2, hcf(B,C)=3 and hcf(A,C)=5. Can you figure out what A, B and C could be?