The sum of three consecutive even number is 84. Let the number be 2*n , 2*n + 2 and 2*n + 4.

We have 2n + 2n + 2 + 2n + 4 = 84

=> 6n + 6 = 84

=> 6n = 84 - 6

=> 6n = 78

=> 2n = 78/3

=> 2n = 26

**The required numbers are 26 , 28 and 30.**

Let the first even integer be x, Then the next even integer is (x+2) and the third is (n+4).

Given that the sum of the three even integers is 84.

Then we will rewrite into an equation as follow:

n + (n+2) + (n+4) = 84

Now we will combine like terms.

==> 3n + 6= 84

Now we will subtract 6 from both sides.

==> 3n = 78

Now we will divide by 3.

==> n= 26

==> n+2 = 28

==> n+4 = 30

**Then, the three consecutive even integers are 26, 28, and 30.**