Well, there's a problem with that right from the outset as it's current rather than voltage which is the issue.
A basic LED is much more of a constant-voltage device. That means they don't conduct much at all until they see about a volt, and then only a small increase in voltage produces a large increase in current, and you can burn the thing out easily. Consequently it's standard practice to use a series resistor to limit the current in the most basic applications.
What confuses things is that what appear to be higher voltage LEDs are in fact hybrid devices - an LED with some sort of driver circuit incorporated. Any LED rated with a forward current limit (up to 60 mA is common) will be 'just' an LED, but where the rating is in volts you can be sure there's a driver circuit incorporated. Those high-brightness LEDs which are becoming common in torches (and bicycle lights) generally have driver circuits. Sometimes you may find an array of LEDs in series with a single driver circuit - again, cycle lamps often have such a set up to give more light without using expensive ultra-high-power LEDs.
In general if there's a driver circuit the device will have a wider tolerance to voltage variation than a filament lamp will, but there's huge variation relating to intended usage and purchase price. The Busch and Muller kit I mentioned above is seriously pricey.
Basic LEDs will produce some light at very low forward currents (1mA), and will be at their most efficient at around 20-30mA, with not much more light being produced as the current increases up to the maximum rating, typically 50 or 60mA, when heat dissipation becomes a problem. If there's a driver then a whole different set of rules applies depending on the design, so it gets complicated!
Rog.
