A group of 12 pirates agree to divide a treasure chest of gold coins among themselves as follows. The k^{\text {th }} pirate to take a share takes \dfrac{k}{12} of the coins that remain in the chest. The number of coins initially in the chest is the smallest number for which this arrangement will allow each pirate to receive a positive whole number of coins. How many coins does the 12^{\text {th }} pirate receive?
Answer Choices
A. 720
B. 1296
C. 1728
D. 1925
E. 3850