You need a voltage source that is greater that the voltage needed by the LED.
2 AA alkaline batteries will give you 3 volts.
That is just barely enough and will make it difficult to power the 2.8 volt LEDs.
If your LEDs will handle 20 milliamps of current, your current limit resistor will be (for 1.8v led):
(3V - 1.8V) / .020 A = 60 ohms
The same 60 resisistor, used in series with the 2.8 volt LED will result in a current of :
(3V - 2.8V) / 60 ohms = .0033 A or 3.3 milliamps. That may not be very bright. If the battery voltage drops much at all, the 2.8V LED will dim to nothing.
You probably know that he LED will only work with voltage of certain polarity. If it doesn't work, you can try hooking it up backwards and see if it works. You can't hurt them if they are hooked up backwards.
Degree in electronics