What are

the consecutive intergers of 2

3,4,5,6,7,8 etc just add one to it to find the next consecutive integer

Let us call x the smallest integer. Because the next two numbers are consecutive even integers, we can call represent them as x + 2 and x + 4. We are told the sum of x, x+2, and x+4 is equal to 72. This means that the integers are 22, 24, and 26.