The UPPER resistor value determines the minimum load current. The minimum load current is 5mA for the more expensive LM117 (the resistor should be 240 ohms or less) and is 10mA for the less expensive LM317 (the resistor should be 120 ohms or less). The upper resistor always has 1.25V across it.What am I following wrong?
The LOWER resistor will have the same current as the upper resistor and Ohm's Law is used to simply calculate its value for setting the output voltage. The output voltage is the voltage across the lower resistor plus 1.25V.