The sum of three consecutive even integers is 54. Find the integers.

Step 1 ：Let's denote the smallest of these integers as x. Because the integers are consecutive and even, the next two integers can be represented as x+2 and x+4.

Step 2 ：The sum of these three integers is given as 54. Therefore, we can set up the equation \(x + (x+2) + (x+4) = 54\).

Step 3 ：Solving this equation will give us the value of x, and consequently, the three integers.

Step 4 ：The solution to the equation is \(x = 16\). Therefore, the three consecutive even integers are 16, 18, and 20.

Step 5 ：Final Answer: The three consecutive even integers are \(\boxed{16}\), \(\boxed{18}\), and \(\boxed{20}\).