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I couldn't find the resistance values for an LED so I tried to measure it and ended up much more confused than before:

I have a plain (red) LED and initially I used a multimeter to measure the resistance but it didn't show any values. I tried 2 multimeters with the same results; also, I tried to connect it the other way around with no improvement. (I do know that the LED isn't broken, it does emit light in a circuit).

So I went another route and added it to a (series) circuit to measure it from there. I have a 3V battery and a 100 ohm resistor, if I measure the current with just those 2 I get 30 mA, which checks out: $$ I = \frac{V}{R} = \frac{3} {100} = 0.003mA $$

But when I add the LED to this circuit (also in series) I measure a current of about 11 mA. Meaning $$ R = \frac{V}{I} = \frac{3} {0.011} = 273\Omega $$ That would be the total resistance and since I know that the resistor has 100 ohm the LED should have a resistance of 173 ohm. This seems like a lot, from reading online I usually see that the default value is 75.

So to double check I swapped the 100 resistor with a 200 ohm one but that confused me a lot: If I measure the current without the LED I get 15mA which aligns with the calculations $$ I = \frac{V}{R} = \frac{3}{200} = 0.015mA$$

but when I add the LED the current drops to about 6mA. Calculating the resistance from there I get $$ R = \frac{V}{I} = \frac{3}{0.006} = 500\Omega$$ So the resistance of the same LED would be 300.

I also tried another approach by measuring the Voltage drop and the results got even more confusing: The voltage dropped by 1.9 for the LED and 1.1 for the resistor; this applies to both the 100 and 200 ohm resistor; I had the same numbers for the 2 resistors which would get me very different numbers using Ohm's law to calculate the resistance.

I know I am doing something wrong but I don't get where my mistake is. Am I messing up the measuring with the multimeter, or am I misunderstanding the formulas, or do I get something more fundamental wrong? My main concern at this point isn't really the LED resistance itself but rather why I am getting such weird values.

Thanks so much to anyone reading all of this!

A LED is a diode, so its "resistance" varies with its voltage dropped between its two terminals.

The equation to use for a LED in series with a resistor is: V_source = V_LED + V_resistor.

In this circumstance, the current is not V_source/ R, as you used, but V_resistor / R

So, to have a crude model, use R around 100 ohm, and measure the voltage drop between the terminals of that resistor. So, if you have a source of 3 volt, and a voltage drop of 1.3 volt for the resistor, you know that you have a voltage drop of 1.7 volt between the terminals of the LED (since the sum must equal 3, the voltage of the source; be sure that the source is at 3 volt, it may be higher if the pile is new, or less if the pile is old).

So, for a crude model of the LED, it is to assume that the LED always drops the constant voltage, here the hypothetical 1.7 volt, whatever the current through it. You can check the validity, the precision, of this model by using a resistor twice smaller ( two 100 ohm in parallel would make 50 ohm). The voltage drop at the terminal of that new 50 ohm resistor should be about the same if the voltage drop at the terminals of the LED stays the same. Check if the measure differs more than it is acceptable for you. If it does, if not, you may need to use the exponential model, which is more difficult to handle for a computation "by hand". But if the precision is good enough for you, you are done: the LED drops a constant voltage (when it is turned ON) and so, has ZERO resistance, just a constant voltage drop.

Note: measure the resistance value of the resistors that you use, they can be close to 100 ohm, as example, but if you measure 97 ohm, use 97, not 100, in your computation.