Two different LED types: diode test on two different multimeters shows just "1"
The diode test function is probably putting out a voltage of 1 to 1.5 V or so. This is below the forward voltage of the LEDs so they will barely light, if at all.

You can check the diode test voltage as follows:


Switch the meter to diode test.
Switch your second meter to DC volts and measure the voltage across the probes of the first meter. That is the voltage being applied to the diode under test.
The '1' is an 'over-range' indication telling you that the voltage on the probes is the test voltage and that not enough current is being drawn. Effectively the probes are open-circuit.
Now switch the second meter to mA and repeat the measurement. You'll probably read a few mA. This is the maximum current your meter supplies on diode test into a short-circuit.


You can swap meters and repeat all the tests to see if they have different test voltages.


  3.3V "popped" the first one I tried: I'm guessing that range is for across their range of LED colours.


No. LEDs need to be driven by controlled current and not connected directly to a voltage supply.



Figure 1. LED current versus voltage for various colours. Source: LED I-V curves.

From the graph we can see that connecting a red LED to a 3.3 V supply would cause the current to go off the chart. A blue LED might survive the experience due to its higher forward voltage, Vf. There's a video I made on the linked page which demonstrates how to draw the graph and you may find it useful.

You might also find Ohm's Law - resistor calculation useful too.



From the comments:


  I understand, but the LEDs said their Vf was "1.8-3.4V", so I put that to the test - if they did work @3.3V, I wouldn't need a resistor, is that right? 


You've already found that you've blown some due to overvoltage so, no, it's not a good idea.


  So my guess was that some colours in their range had a Vf of 3.4 V. 


Yes, but at what current and what is the variation? See Variations in Vf and binning for more on this.


  Is that graph true for all types of LEDs - all red LEDs are the same?


No. I generated it from datasheets for specific LEDs. We recommend, "No datasheet? No sale!" for reasons that you are learning.


  Wouldn't I need to know the max forward current here? (I don't have Vf or Ifmax.)


Yes, but 20 mA is safe for most 3 mm or 5 mm LEDs.

To measure the Vf you can do a simple test.







simulate this circuit &ndash; Schematic created using CircuitLab

Figure 2. A simple Vf measurement circuit. DUT is the "diode under test". VM1 can be your multimeter on V DC range.

The 560 &Omega; resistor will limit the current through the LED to about 10 mA. (Actually, for a 2 V LED the current will be about 12.5 mA and for a 3.5 V LED the current will be about 9.8 mA. This will be good enough for most purposes.)