Do you not need a resistor in that circuit?
In order for the LEDs to last for a longer period of time (their rated hours limit), you will need to use the resistor, or some other power-draining device with the same resistance as the resistor.
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While you don't have to put a resistor in that circuit, putting one it could help. As it stands right now the forward voltage of the LED is likely somewhere in the 1.5 - 2.7 volt range, and the internal resistance of the battery is somewhere in the range of 10ohms to 100ohms. This means that the current across the led will vary a bit as the battery begins to drain. Adding a resistor would limit the current more and therefore result in the battery lasting a longer time. So although this circuit does work, it is not the best design, especially if you want it to last a long time.