What is the greatest common denominator of 24 and 36?

Answer 1

There can be no greatest common denominator.

For supose x is the greatest common denominator.

ie 24 divides x and 36 divides x.

Then 2x is a common denominator and 2x > x so 2x is a greater common denominator than the greatest common denominator. That contradiction implies that there is no greatest common denominator.

Answer 2

The greatest common denominator of any set of denominators is infinite.

Answer 3

2