2 AA cells in series will start at around 3V but the voltage will steadily drop as the cells discharge and they are not considered totally flat until they are down to 2V (1V per cell).
The LEDs will dim and eventually just about go out well before the batteries are flat.
Three cells would be better, you would get a nearer to constant light and be able to use the cells until they were truly dead.
To work out the resistor needed for a given voltage:
Subtract the LED forward voltage from the supply voltage, then divide that result by the LED rated current:
eg. a 20mA [0.02 Amp] LED with a 1.8V forward voltage on 3V:
Porbably not. The LED was rated at 2.0V-2.2V. The current was not mentioned but most 5mm LEDs are rated at 20mA with 30mA as the maximum allowed current. Your current of 100mA will soon burn them out.
The resistor should be (3V - 2V)/20mA= 50 ohms, 51 ohms is the nearest ordinary value.