Here is my finished three channel constant current LED driver.

Specs:
Three LM317T adjustable voltage regulators, configured in constant current variable voltage mode.
Six one-watt 10 ohm resistors, wired in parallel for 5 ohm loads on the adjust pin of the regulator.
Three 1uF smoothing capacitors on the regulator output, one 100nF filter capacitor on the power connection.
Each channel is configured for 250 mA, which is 100 ma less than my leds can handle, but, this is good enough for a start - I have proper sized resistors on order. I will probably make a PCB for the second iteration of this project, and I'll be using a single resistor instead of two in parallel.
The six pin connector goes to the LED module, the five pin connector is the power and control lines from my rgb led controller.

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