Actually, white light produced by LEDs are not a flat distribution of wavelengths. They use a phosphorus layer to convert a base wavelength into a set of wavelengths.
The primary color output by the LED element is still the dominant color emitted. You can see a big spike around 450nm here:
https://www.lrc.rpi.edu/programs/nlpip/lightinganswers/led/whiteLight.asp
