The mean of three consecutive odd integers is 27, the largest among the integers is.

29

If the average/mean of 3 consecutive odd integers is 27, then their sum is 27 × 3 = 81

Let the three even integers be x – 2, x and x + 2.

So we get the equation as x – 2 + x + x + 2 = 81.

x = 27.

So the three integers are 25, 12 and 29.

Hence the largest number = 29

Alternate Short cut: 

The average/mean of 3 consecutive odd integers is 27, then the numbers will be : (27 - 2), 27, (27 + 2) ⇒ 25, 27, 29

Hence the largest number =29