So you got the common anode type LED. They are easier to hook up to transistors than common cathode ones. The illustration shows the pin mapping for both.
What the diagram is trying to say is that the LED comes in two varieties, one common anode, the other common cathode.
You could put a single resistor on the common. I've done that when playing around. But you really want to put one on each color, so that you can vary the current flowing to each independently, and thus "level" the brightness of each color.