The benefit of LED is longer lifetime than incandescent lamp, and even higher efficiency in latest LED technology. LED is also very compact, but unfortunately it needs higher voltage to operate. A single cell battery (1.5v) or rechargeable  cell (1.2V) cannot be used to power LED directly. We have to use a DC-to-DC step-up converter to enable single cell operation for LED, a schematic diagram below shows one of  the circuit:

LED Power Supply for AA Cell circuit schematic

For more information about this single cell LED circuit, you can read at this circuit’s schematic diagram source.