How do you find 3 consecutive integers such that their sum is 27 less than three times the smallest?

Call the smallest $n$; you have:
$n + \left(n + 1\right) + \left(n + 2\right) = 27 - 3 n$
$3 n + 3 = 27 - 3 n$
$6 n = 24$
$n = 4$
4+5+6=15=27-(3×4)=27-12=15