Well it's plausible but the numbers seem suspicious (I think). Your meter's manual refers to measuring capacitance/resistance in "parallel mode" by default, but that this can be changed to "series mode". This suggests that it is trying to compute the equivalent parallel resistance of the network. The real part of the impedance of a parallel RC network is
\$\frac{R}{1+\omega^2R^2C^2}\$
... and this is frequency dependant. The equivalent parallel resistance in this case is constant with frequency (by definition it is R) and this is what I would expect the meter to display. However in a real capacitor, the equivalent shunt resistance is not formed by a real resistor.
It would be interesting to switch to "series mode" if possible and see what the numbers are then.
The only reason DMMs can't measure inductances is that it is more difficult to measure inductance than resistance or capacitance: this task requires special circuitry, which is not cheap. Since there are relatively few occasions when inductance measurements are required, standard DMMs do not have this functionality, which allows for lower cost.
Simple DMMs can measure capacitance by just charging the capacitor with a constant current and measuring the rate of voltage build-up. This simple technique provides surprisingly good accuracy and wide dynamic range, therefore it can be implemented in almost any DMM, without significant cost penalties. There are other techniques as well.
Theoretically, one could measure inductance by applying a constant voltage across an inductor and measuring the current build-up; however, in practice this technique is much more complicated to implement, and the accuracy is not that good as for capacitors due to the following reasons:
- Inductors may have relatively high parasitic resistance and capacitance
- Core losses (in cored inductors)
- EMI (incl. stray inductance and capacitance)
- Frequency dependent effects in inductors
- More
There are few techniques for measuring inductances (some of them are described here).
LCRs are special meters designed for inductance measurements and containing the required circuitry. These are costly tools.
Since the hardware for measuring the inductance may also be used for accurate measurement of R and C, LCRs also employ this circuitry in order to improve the accuracy of capacitance and resistance measurements (for example: AC resistance, AC capacitance, ESR etc.). I believe that the difference between measuring inductance and capacitance with LCR is just a matter of different firmware algorithms, though it is just a guess.
Therefore, the general answer to your question is "yes, LCRs are usually more accurate in RC measurements than DMMs, and they can measure a wider range of measurable quantities". However, this is just a rule of thumb - there are many superb DMMs and lousy LCRs out there... Read specs.
Best Answer
Absolutely. You will need a variable-frequency oscillator, often called a function generator, though, and a meter of some sort (DMM or oscilloscope). Connect the oscillator (set up for sine waves, please), the inductor, and a resistor like this
simulate this circuit – Schematic created using CircuitLab
Start at very low frequency, and the voltage at the test point should be zero, or very close. Increase the frequency and the voltage at the test point will rise. Find the frequency at which the voltage at the test point is one half the voltage at the oscillator. Depending on the frequencies available, you may have to try different resistor values to find one which works. Call this frequency f. Then, since the impedance Z of the inductor can be written as $$Z = 2\pi f L $$ and for equal voltages across Z and R, Z = R $$R = 2\pi f L $$ and $$L = \frac{R}{2\pi f} $$ This will be true for what are called high-Q inductors, which have a low series resistance, and for low-Q resistors the problem becomes a good deal more complicated, but it's a good place to start. Also note that this value of L is only correct for this frequency. For something other than a high-Q inductor, the results will vary (a little or a lot) with frequency.