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**Soroban** Hello, Sott!

We have: .$\displaystyle \begin{array}{cccccc}1&A&B&C&D & E \\ \times &&&&& 3 \\ \hline A&B&C&D& E & 1 \end{array}$

We see that $\displaystyle E = 7.$

We have: .$\displaystyle \begin{array}{cccccc}1&A&B&C&D&7 \\ \times &&&&& 3 \\ \hline A&B&C&D& 7 & 1 \end{array}$

We see that $\displaystyle D = 5.$

We have: .$\displaystyle \begin{array}{cccccc}1&A&B&C&5&7 \\ \times &&&&& 3 \\ \hline A&B&C&5& 7 & 1 \end{array}$

We see that $\displaystyle C = 8.$

We have: .$\displaystyle \begin{array}{cccccc}1&A&B&8&5&7 \\ \times &&&&& 3 \\ \hline A&B&8&5& 7 & 1 \end{array}$

We see that $\displaystyle B = 2.$

We have: .$\displaystyle \begin{array}{cccccc}1&A&2&8&5&7 \\ \times &&&&& 3 \\ \hline A&2&8&5& 7 & 1 \end{array}$

We see that $\displaystyle A = 4.$

We have: .$\displaystyle \begin{array}{cccccc}1&4&2&8&5&7 \\ \times &&&&& 3 \\ \hline 4&2&8&5& 7 & 1 \end{array}$

The smallest such number is $\displaystyle 142857.$