Let us assume the smallest of the three consecutive integers = x
Then
The middle integer among the three consecutive integers will be = x + 1
The biggest integer among the three consecutive integers will be = x + 2
The sum of the three consecutive integers is already given in the question and it is -165.
Then
x + x + 1 + x + 2 = - 165
3x + 3 = - 165
3x = - 165 - 3
3x = - 168
x = - (168/3)
= - 56
So the integer that is closest to zero is - 56. This is the answer you were looking for hopefully. The other integers will obviously be at a greater distance from zero.