In this paper, we design linear precoders for the downlink of a visible light communication (VLC) system that simultaneously serves multiple users. Instead of using phosphor-coated white light-emitting diodes (PWLEDs), we focus on Red-Green-Blue light-emitting diodes (RGB-LEDs) that allow modulating three separate data streams on the three primary colors of the RGB-LEDs. For this system, we design a zero-forcing (ZF) precoder that maximizes the weighted sum rate for a multilevel pulse amplitude modulation (M-PAM). The precoding design in RGB-based systems presents some challenges due to the system constraints, such as the limited power, the non-negative amplitude constraints per light-emitting diode (LED), and the need to guarantee white light emission while transmitting with RGB-LEDs. For comparison purposes, we also consider the ZF design for a PWLED-based system and evaluate the performance of both a PWLED- and an RGB-based system.