2000 AMC 12 Problem 16

A checkerboard of 13 rows and 17 columns has a number written in each square, beginning in the upper left corner, so that the first row is numbered 1,2,\ldots,17, the second row 18,19,\ldots,34, and so on down the board. If the board is renumbered so that the left column, top to bottom, is 1,2,\ldots,13, the second column 14,15,\ldots,26 and so on across the board, some squares have the same numbers in both numbering systems. Find the sum of the numbers in these squares (under either system).

\textbf {(A)}\ 222 \qquad \textbf {(B)}\ 333\qquad \textbf {(C)}\ 444 \qquad \textbf {(D)}\ 555 \qquad \textbf {(E)}\ 666

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.