In many wireless communication applications, it is desirable to transmit the same data to multiple user equipments (UEs). Physical layer multicasting presents an efficient transmission topology to exploit the beamforming capabilities at the transmitting nodes and broadcast nature of the wireless channel to satisfy the demand for the same content from several UEs. An advantage of multicasting is to avoid unnecessary co-channel interference between UEs requesting the same data. The difficulty is to find the suitable beamforming configuration that guarantees an acceptable minimum data rate, among the receiving UE group, to the multicast transmission. This paper addresses the max-min fair multigroup multicast optimization problem and proposes a novel iterative elimination procedure coupled with semidefinite relaxation (SDR) to find the near-optimal rank-1 beamforming vectors in a cell-free massive MIMO (multiple-input multiple-output) network. The proposed optimization procedure significantly improves computational complexity and spectral efficiency compared to common methods that use SDR followed by some randomization procedure and the state-of-the-art difference-of-convex approximation algorithm. The importance of the proposed procedure is that it is applicable to any SDR problem where a low-rank solution is desirable. Further, we propose a low-complexity algorithm that achieves 87% of the optimal rank-1 solution at orders-of-magnitude lower computational time.