Ok, I'm going to attempt a thought experiment involving public math and an undetermined outcome. Lets see how well I foul it up. (and I'm doing it on a phone, so beware autocratic ions)
Lets assume three identical LEDs with a constant dynamic resistance of 0.1V/5mA (20 ohms) for currents between 5 and 20mA. Other than the LEDs being identical, I think this is a reasonable model of reality.
If one LED with an unknown resistance in series with it draws 15mA, what does that value of resistance need to be to cause three in parallel to draw 21mA?
So, we see a drop in current through the LEDs of 8mA, suggesting a drop in voltage of 0.16V.
So what value resistor will drop an additional 0.16V when the current increases by 7mA?
That would be about 23 ohms.
Assuming the meter is on a 100mA range, this would imply a burden voltage of around 2.3V, which is atypical for this sort of range.
Interestingly, it also implies (I think) that in this case the series resistance is very close to the dynamic resistance of the LEDs.
If you have two multimeters and can measure the voltage across the ammeter while measuring the current through the LED(s), or measure the voltage across the LED(s) while measuring the current through them we can get more information on both the burden voltage and the dynamic resistance (you will need 2 measurements at different current for the latter)