Final answer:
The largest number is 38.
Step-by-step explanation:
To find the largest number, let's assume the smallest number as 'x'. The consecutive even integers would then be x, x+2, and x+4. We can write the equation as x + (x+2) + (x+4) = 108. Solving this equation gives us 3x + 6 = 108. Subtracting 6 from both sides, we get 3x = 102. Dividing both sides by 3, we find that x = 34. Therefore, the largest number is 34+4 = 38.
Learn more about finding the largest number among consecutive even integers