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 us by showing us three numbers for which it's false -- in other words, show us three integers such that every pair have a common divisor greater than 1, but all three numbers don't have a common divisor greater than 1.

(01.03 mc) which of the following is a step in simplifying the expression x multiplied by y to the power of 2 over x to the power of negative 3 multiplied by y to the power of 3, the whole to the power of negative 4. select one: a. x to the power of negative 4 multiplied by y to the power of negative 2, the whole over x to the power of negative 7 multiplied by y to the power of negative 1. b. x to the power of negative 4 multiplied by y to the power of negative 8, the whole over x to the power of 12 multiplied by y to the power of negative 12. c. x to the power of negative 4 multiplied by y to the power of negative 8, the whole over x to the power of negative 3 multiplied by y to the power of 3. d. x to the power of negative 4 multiplied by y to the power of negative 2, the whole over x to the power of negative 3 multiplied by y to the power of 3.