Answer :

Consecutive integers mean one after the other and their difference would one more or less.

Let the numbers be x, x +1, x +2.

Therefore x + (x+1) + (x +2) = 567
               3x + 3 = 567
               3x = 567 -3 = 564
               3x = 564  Divide by 3.
                 x  = 564/3
                 x  = 188
Therefore integers  x, x +1, x +2 = 188, 188+1, 188+2.
                                                =  188, 189, 190.
Cheers.

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