When expanded as a decimal, the fraction $\frac{1}{7}$ has a repetend (the repeating part of the decimal) of $142857$. The last three digits of the repetend are $857$.
When expanded as a decimal, the fraction $\frac{1}{13}$ has a repetend that is $6$ digits long. If the last three digits of the repetend are $ABC$, compute the digits $A$, $B$, and $C$.
Try to do long division with 1÷13. If you do that you should get that 113=0.¯076923
Therefore, (A,B,C)=(9,2,3)