Consecutive odd integers differ by two, so we may let n - 1, n + 1, and n + 3 be the three consecutive odd integers. The least of these integers is n - 1 and the greatest is n + 3. Thus

2(n - 1) = 3(n + 3) + 15

2n - 2 = 3n + 9 + 15

2n - 2 = 3n + 24

2n - 3n = 2 + 24

-n = 26

n = -26

The three integers are thus -27, -25, and -23.