The Mysterious Number

Number Theory Level 1

Each letter in the following cryptogram represents a distinct, non-zero digit: $\begin{array}{ccccccc} & A & B & C & D & E & F \\ \times & & & & & & 3 \\ \hline & B & C & D & E & F & A. \end{array}$ What is $A+B+C+D+E+F?$