LM317 Resistor Values Performance
Resistor effects in an LM317 are largely covered in the LM317 data sheet
 Comments below will use data from this datasheet. Check the datasheet used for your specific device if running "close to the wire". 

Note!: For your designs to ALWAYS work correctly, worst case values must be used.
If you want your design to typically work (but not always) you can design wityh typical values :-). Note than sometimes worst case will be the minimum value and sometimes the maximum value, depending on what is being designed. 



There are two main factors in setting the maximum LM317 resistor values:

(1) The LM317 has a MINIMUM OUTPUT CURRENT.   

If this current is not drawn the IC will not operate correctly.
 This current can be met by always having a minimum load resistor but the normal practice is to ensure that R1 - the resistor from Output to Adj - is small enough to ensure that
  I_R1 >= I_out_min ,
 so as Vout - Vadj = 1.20V_min when the IC is working correctly,
 R1 &lt;= V/I &lt;= 1.20 / I_out_min_max.

I_out_min_max here means that there is a minimum value that Iout must have and this is the maximum value that I_out_min must have. 

I_out_minimum = 3.5 mA typical, 12 mA maximum !!!!!!!!!!!!!!
 So R1 &lt;= Vadj_min / Iout_min_max :-) = 1.20/0.012A = 100 Ohms MAX !!!!!!!!!!!!!!

Many LM317 circuits use R1 > 100 ohms.
 This value only applies at I_out_min_max.
 For I_out_min_typ = 3.5 mA R1 can be about 330 Ohms.

(2) Error in Vout caused by Iadj in R2.

A data sheet specified current flows "out" of Vadj. Call this Iadj.
 Where a resistor R2 is provided from Vadj to ground to increase Vout, this current flows through R2 and increases the output voltage. Variations in this current will vary Vout. If it is desired to set Vout accurately then the effect of both the typical value and variation in value of this current need to be taken into account.

Vout = Vadj x (R1 + R2) / R1 + Iadj x R2.  

Iadj = 46 uA typical, 100 uA maximum.
 Vadj = Vref = 1.20 / 1.25 / 1.30 V min / typ / max

So IF R1 is &lt;= 100 ohms at 1.2V then ohms per Volt = 100/1.2 = 83 ohms per volt of output.
  This applies to voltage across R1 or R2.
 Error voltage in R2 per volt of output = I x R = 100 uA x 83 ohms = 8.3 mV.
 ie error due to Iadj is + 0.83% at Iadj_max IF R1 is set at maximum allowed for Iout_min.

** &lt;> TANTALUM CAPACITORS!**  NB: The diagram copied below shows tantalum capacitors. Those who wish their circuits to live long and prosper will NOT use tantalum capacitors here, especially not for the input capacitor. Tantalum capacitors in high energy circuits, such as power supplies, when subject to even very very (uS range) over voltage spikes, will break down and self immolate. Can be amusing "on the bench". Not usually so amusing "in the field".



Here I've used 1.2V as that is Vadj min but it is actually in the range  1.2 - 1.3V





Related.

LM317 has an Iout related minimum (Vin-Vout) = dropout voltage.
 See diagram below.
 This is often not properly allowed for.



E&amp;OE