Step 2: How it works
Ohm's law says that U/I=R, which means that Voltage divided by Ampere makes resistance.
so if you want to connect one or more luxeon 1W LEDs, which has a power consumption of 350mA, the calculation should look like this: 1,25 (the constant reference voltage of the LM317) divided by 0,350 (the LEDs power consumption) makes 3,57. So if the resistor is 3,57, constant current will be 350mA. The closest E12 value is 3,9 ohms, it will give you a constant current of 321mA. However you can't see any difference in the light output.
If you use 3W LEDs, which has a current consumption of 700mA, the calculation should be: 1,25 divided by 0,7 makes 1,78. The closest E12 value is 1,8 ohms, the output will be 694mA
the resistor must be at least 1W in both calculations.
Although the LM317 is rated for 1,5 Ampere, I wouldn't recommend it for applications that need more than 1 Amperes, because it gets very, VERY hot. the LM350 is equal to the LM317, but it's rated for 3 Amps