Let the three consecutive even numbers be:

• $x$ (the first even number)
• $x + 2$ (the second even number)
• $x + 4$ (the third even number)

The sum of these numbers is given as 1524. Therefore, the equation becomes:

$x + (x + 2) + (x + 4) = 1524$

Now, let's simplify the equation:

$3x + 6 = 1524$

Subtract 6 from both sides:

$3x = 1518$

Divide both sides by 3:

$x = 506$

So, the three consecutive even numbers are:

1. First number: $506$
2. Second number: $506 + 2 = 508$
3. Third number: $506 + 4 = 510$

Thus, the three consecutive even numbers are 506, 508, and 510.

Would you like further details or explanations on this?

Here are some related questions to consider:

1. What is the general formula for the sum of any three consecutive even numbers?
2. How would you solve for consecutive odd numbers instead?
3. How can you check if the sum of three numbers is divisible by 3?
4. What if the sum was an odd number—how would the approach change?
5. How can this problem be extended to four consecutive even numbers?

Tip: When solving for consecutive numbers, use variables that take into account the pattern (e.g., $x, x + 2, x + 4$ for evens).