AMC 12A 2019 Problem 11

For some positive integer k, the repeating base- k representation of the (base-ten) fraction \dfrac{7}{51} is 0 . \overline{23}_{k}=0.232323 \ldots k. What is k ?

Answer Choices
A. 13
B. 14
C. 15
D. 16
E. 17