If you check the data sheets for the LM317...
You will see that the (K) is the TO-3 case and the (T) is
the TO-220 case that most of the members here use...
As Jerry stated, you should use the LM317T.
If you are pushing it at higher current, you will need a heat-sink for the regulator, using the (T) case you have a hole to bolt the H/S on, with the (K), you will have to use thermal adhesive.
Plus the (K) takes up a lot more room.