The blues and reds are in the spectrum produced by the white leds. The ratios may not be perfect but it does the job.
A little bit of green (our eyes are particularly sensitive to green) will quickly shift blurple (red+blue) into a whitish hue.
Take a look at this thread for some different spectra produced by some LED fixtures. Particularly look at the Fluence Vypr and Spydr spectrums which are mostly white LEDs and looks like white light.
Don’t be afraid of LED fixtures that produce a white spectrum.