The three consecutive odd integers can be written as:

2x - 1, 2x + 1, 2x + 3, where x is integer

2x - 1 is the smallest integer

Three times the smallest is 27 more than the sum of the other two:

3(2x - 1) = 27 + (2x + 1) + (2x + 3)

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x = 17

2*17 - 1 = 33

33 + 2 = 35

35 + 2 = 37

The three consecutive odd integers are 33, 35 and 37.