The sum of three consecutive even numbers is 36. Find the largest of these numbers.

Let the first even number be $x$.
The second consecutive even number will be $x+2$.
The third consecutive even number will be $x+4$.

The sum of the three numbers is 36:

Combine like terms:

Subtract 6 from both sides:

Divide by 3:

The three consecutive even numbers are $x$, $x+2$, and $x+4$.
Substituting $x=10$:
First number: 10
Second number: $10+2 = 12$
Third number: $10+4 = 14$
The bigger number is 14.

The bigger number is 14.