6. (10 points) Fill in the 6 boxes in the figure with the numbers $1 \sim 6$ respectively, the smallest result that can be obtained is $\qquad$

Translate the above text into English, please retain the original text's line breaks and format, and output the translation result directly.
【Answer】Solution: The smallest 1 and 2, placed in the tens place, the remaining 3 and 1 form 13, 2 and 4 form 24, and finally 5 and 6 form the equation $5 \times 6$, so the smallest result is:
$$
\begin{array}{l}
13 \times 24+5 \times 6 \\
=312+30 \\
=342
\end{array}
$$

Answer: The smallest result that can be obtained is 342.
Therefore, the answer is: 342.