How many you need depends upon the LED type you use and how much light you need. There are some very high brightness types that may only require a few (or even one). The standard high brightness types would likely require several to a dozen or more. I have seen some LED lamps that operate directly from 110V and use about a dozen LEDs which is stated to give the brightness of about a 30W bulb. Since the light from the LEDs is directional, I'm sure that's enough light to read by.
Since they are already directional, why would you want to add a reflector? A diffuser might be more appropriate.