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