There's 2 different things that you have to consider... voltage and current (amps). 9V batteries are just that, 9Vs.. AA, AAA, D, C etc. are all 1.5 Volts. So to make 9V you need to connect 6 1.5 volt batteries in "series", i.e. plus to negative ends so you get 1.5 + 1.5 + 1.5 + 1.5 + 1.5 + 1.5 = 9
If your LED needs 3 volts, then you can't use a 9V or you'll fry them.. UNLESS you use a resistor in between the battery and the LEDs in order to reduce the voltage the LED will actually "see".
To power a 3V LED, you would connect 2 AA in series to get the 3Volts. Now here's the thing. Each LED will require a certain amount of current in order to glow, not just the 3volts. So if you hook up a bunch of LEDs (in parallel), they'll all require 3volts but they'll draw even more current than a single LED, and thus drain your batteries a hell of a lot faster. So in this case you'd want to connect more batteries in "parallel" in order to supply more power.
AA, AAA, C, D - all 1.5 volts and just different sizes that have come about over time. Also, although I haven't checked, the larger batteries can probably supply more current than the smaller ones.
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