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Most LED's are 1.5-3.5V your standard LEd's in general are 1.5
High intensity LED's those that have a MCD of 2000-3500.
The higher intensity Led's will work at lower voltages but they will not be as bright.
http://www.datrecords.com/images/Parts/BLK_xl.jpg
If you are speaking of the mod in the link above having a color changing Led would not be effective as a solid color LED.
I will admint I know nothing of hte sidnificance of adding a LED to the dial except for cool factor. If it is used for lighting in dark rooms when playing then a solid color would be prudent.
As a cool effect across the player the color changeing LED would be neat. If there is room have 2 color changers installed since they do not work always at the same timeing there would allways be a light on.
Or you could go with a bit heavier duty light effect
Neon light rope
This is a light string 3 mm thick or about the thickness of a chain that holds down the pens at your local bank.
You can cut /bend twist the neon light rope and practially any direction you want
example one
example two
They are not great pictures but were done in complete darkness with no flash.
For your usage
You could take the rope rope and loop it around the complete turntable. Just glue it in place around the platter. You could even cut a length and attach it to the tone arm.