56+57+58=171
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There are two consecutive odd integers whose sum is 340. They are 169 and 171.
The sum of any three consecutive odd integers is going to give an odd result. It is impossible for the sum of an odd number of odd integers to equal an even number.
Divide the sum of the three consecutive odd integers by 3: -273 /3 = -91. The smallest of these integers will be two less than -91 and the largest will be two more than -91, so the three consecutive odd integers will be -89, -91, and -93.
Divide the sum of the three consecutive odd integers by 3: -147 /3 = -49. The smallest of these integers will be two less than -49 and the largest will be two more than -49, so the three consecutive odd integers will be -47, -49, and -51.
Divide the sum of the three consecutive odd integers by 3: 45/3 = 15. The smallest of these integers will be two less than 15 and the largest will be two more than 15, so the three consecutive odd integers will be 13, 15, and 17.