Let's denote the three consecutive even numbers as $x$, $x + 2$, and $x + 4$. The problem states that the sum of these three numbers is 138. So, we can set up the following equation:

$x + (x + 2) + (x + 4) = 138$

Simplify the equation:

$3x + 6 = 138$

Next, subtract 6 from both sides to isolate the term with $x$:

$3x = 132$

Now, divide both sides by 3:

$x = 44$

So, the smallest of the three consecutive even numbers is $\boxed{44}$.

Would you like more details on how this was solved?

Here are some related questions you might find interesting:

1. What are the other two even numbers in this sequence?
2. How do you solve for three consecutive odd numbers given their sum?
3. What if the sum was 180? What would be the smallest even number?
4. How would the solution change if the numbers were consecutive odd numbers?
5. What is the sum of the next three consecutive even numbers after 44, 46, and 48?

Tip: Consecutive even or odd numbers can be represented as $x$, $x + 2$, $x + 4$, etc., making it easier to set up and solve equations.