To find the largest of three consecutive even numbers whose sum is 408, we can follow these steps:

1. Let's denote the three consecutive even numbers as $x$, $x+2$, and $x+4$.

2. Write an equation for their sum: $x + (x+2) + (x+4) = 408$

3. Combine like terms: $3x + 6 = 408$

4. Subtract 6 from both sides of the equation: $3x = 402$

5. Divide both sides by 3: $x = 134$

6. The three consecutive even numbers are $134$, $136$, and $138$.

Therefore, the largest number is $138$.

Would you like more details or have any questions?

Here are 8 related questions for further practice:

1. The sum of 3 consecutive odd numbers is 315. What is the largest number?
2. If the sum of 4 consecutive even numbers is 520, find the largest number.
3. Three consecutive integers sum up to 72. What is the smallest integer?
4. The sum of four consecutive odd numbers is 160. What is the smallest number?
5. The sum of five consecutive even numbers is 450. What is the middle number?
6. Find three consecutive integers whose sum is 117.
7. If the sum of three consecutive multiples of 3 is 81, what are the numbers?
8. Three consecutive numbers sum up to 90. What is the largest number?

Tip: When dealing with consecutive numbers, set up the equations carefully to ensure you account for the pattern in the sequence.