Multi-Color LED and Resistors...?

Hi,
I have a display that I am planning on using a single LED (Red, Green, Blue) to indicate the position of the (on-on-on) toggle switch. Example would be in the down position the LED would show GREEN, Middle position the LED would show Blue, Up position it would be RED.

My question is: will I need to put a resistor on each color lead of the LED or would just one on the Cathode (NEG) lead be good enough to handle the power coming from each of the Anode (POS) leads?

I am just starting out in this world and any help would be greatly appreciated…
Thanks,
Brian

If only one will ever be turned on at a time, then a single resister on the common pin is fine.

You will discover that Red has a lower Vf than Blue or Green, so you need to select the resistor value for that, which may make the Blue and Green dimmer than you expected.
(5V - 2.2V)/.02A = R ohms
That same with Blue/Green:
(5V - 3.5V)/R = lower mA number.