Answer
$16,~18,~20$
Work Step by Step
Three consecutive even integers can be written as:
$$2n, ~2n+2,~2n+4$$
Their sum is $54$:
$$2n+2n+2+2n+4=54$$
Collect like terms:
$$6n+6=54$$
Solve for $n$:
$$6n=54-6$$
$$6n=48$$
$$n=\frac{48}{6}=8$$
These numbers are:
$$2\cdot 8,~2\cdot 8+2,~2\cdot 8+4$$
$$16,~18,~20$$
