The extra resistor would be connected across the two ends of the potentiometer. As supplied, a 2 kOhm pot has too much resistance to limit the output to 15 Volts.
The total value of the paralleled resistor/potentiometer is derived from the LM317 datasheet formula:
V
out = 1.25V x (1 + (R
pot/R1)) + I
adj x R
potThe last term compensates for the current flow from the adjust terminal, which is small enough to ignore.
So the simplified formula reduces to:
V
out = 1.25V x (1 + (R
pot/R1))
Substituting 147 Ohms for R1 and solving for R
pot, we arrive at 1610 Ohms, which limits V
out to 15 Volts.
By adding a resistance in parallel with the potentiometer, we can "trim" the maximum value.
Take the reciprocal of 1610 Ohms, subtract the reciprocal of 2380 Ohms, then find the reciprocal of the result.
That value represents the amount of parallel resistance to reduce the total to the calculated value of 1610 Ohms.
As for the result of that calculation, I'll leave that as an exercise for the student.
Do post your result.
RF+ Tech
Edited for better clarity