Adam wrote the numbers from 1 to 9 into a $3 \times 3$ table as shown in the image:

| 7 | 6 | 4 |
| :--- | :--- | :--- |
| 1 | 2 | 8 |
| 9 | 3 | 5 |

For this filling, the sum of the numbers in the three cells along each side is always the same. Adam found that the numbers can be filled into the table in other ways without breaking the property of having the same sums along the sides.

What is the smallest value that this sum can have? Provide an example of a table with the smallest sum along the sides and explain why it cannot be smaller.

(J. Tkadlec)