There are generally two constraints. The series pair of

resistors must consume at least the regulator minimum output

current, if the regulator must work all the way to zero

external load. And the divider voltage must be the desired

output voltage minus the nominal difference voltage between

the output and the reference pin.

A secondary constraint is that the range of current passed

through the reference pin does not distort the divider

voltage too much.

For the LM317Lhttp://

www.onsemi.com/pub/Collateral/LM317L-D.PDF
the maximum value of the minimum output current allowed if

you expect the regulator to regulate is 10 mA, so if you

will not always have at least that much external load, then

the divider must consume it. Since the nominal difference

between the reference pin voltage and the output voltage is

1.25 volts, there will be that much voltage across the top

resistor of the reference divider, so it must be no more

than 1.25/.01=125 ohms. If you use the typical value of

minimum load current or 3 mA, instead of the worst case

(usually okay for a single system that will not be

manufactured in high volume) that resistor rises to

1.25/.003=417 ohms. Usually, any value between those will

work. I notice that the example on the sheet uses 240 ohms.

Then the bottom divider resistor must drop the rest of the

desired output voltage, or 3.3-1.25=2.05 volts, in this

case, while it also passes the reference pin (adjustment

pin) current of about 50 uA. Since the first resistor is

delivering 3 to 10 mA, the additional current from the

reference pin may be within the tolerance effect of the

resistors.

Ignoring the reference pin current and assuming you use 240

ohms as the upper resistor

(delivering about 1.25/240=5.2 mA), the lower one would be

2.05/.0052=394 ohms.

All this process is described in detail starting on page 8.