In this paper, practical utilization of multiple distributed reconfigurable intelligent surfaces (RISs), which are able to conduct group-specific operations, for multi-group multicasting systems is investigated. To tackle the inter-group interference issue in the multi-group multicasting systems, the block diagonalization (BD)-based beamforming is considered first. Without any inter-group interference after the BD operation, the multiple distributed RISs are operated to maximize the minimum rate for each group. Since the computational complexity of the BD-based beamforming can be too high, a multicasting tailored zero-forcing (MTZF) beamforming technique is proposed to efficiently suppress the inter-group interference, and the novel design for the multiple RISs that makes up for the inevitable loss of MTZF beamforming is also described. Effective closed-form solutions for the loss minimizing RIS operations are obtained with basic linear operations, making the proposed MTZF beamforming-based RIS design highly practical. Numerical results show that the BD-based approach has ability to achieve high sum-rate, but it is useful only when the base station deploys large antenna arrays. Even with the small number of antennas, the MTZF beamforming-based approach outperforms the other schemes in terms of the sum-rate while the technique requires low computational complexity. The results also prove that the proposed techniques can work with the minimum rate requirement for each group.