In this paper, we study linear transceiver designs for indoor visible light communications (VLCs) with multiple light emitting diodes (LEDs). Specifically, we investigate VLCs including white emitting diodes and VLCs including red/green/blue (RGB) LEDs. The transmitter precoding and the offset are jointly designed by considering certain key practical lighting constraints, such as optical power, non-negativeness, and color illumination. Various non-convex transceiver design problems are formulated aiming to minimize total mean-squareerror to improve transmission reliability. We show that for multi-input single-output white VLCs, the optimal precoding reduces to a simple LED selection strategy. For multi-input multioutput (MIMO) white VLCs, we prove that the optimization problem with multiple constraints can be equivalently simplified to a problem with single constraint, which enables us to propose efficient algorithms to search local optimal solutions. For MIMO RGB VLCs, by using certain useful transformations, we show that the precoding design is equivalent to covariance matrix design of transmit signals, which can be further transformed to a convex optimization problem. To develop an algorithm to find the optimal solution, we derive the optimal structure of the covariance matrix and show that the optimal solution can be obtained via a water-filling approach. Extensive simulation results are provided to verify the performance of the proposed designs.