38; 39; 40!
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The square roots of 117 are irrational numbers and so are not two integers - consecutive or otherwise.
The numbers are 38, 39, and 40.
The numbers are 37, 39 and 41.
The first ten consecutive composite positive integers are: 114 115 116 117 118 119 120 121 122 123
Three consecutive integers whose sum is 117 are 38, 39, and 40. N + (N+1) + (N+2) = 117 3N + 3 = 117 3N = 114 N = 38