We want to find the current flowing through the LED, which is the same as the current flowing through the resistor. We can use Ohm's Law to figure out the current through the resistor. We first need to find the voltage across the resistor:

Using Ohm's Law, we can substitute 3.0 V for V and 15 mA for I:

Solve for R, and we find the resistor value:

That means we need a resistor value of 200 Ω or greater to limit the current through the LED to no more than 15 mA.