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?
i would greatly appreciate it if someone responded!