The problem of transmitting a common message over a multiple-input multiple-output (MIMO) Gaussian broadcast channel with multiple receivers is well understood in terms of capacity. Nevertheless, existing optimal (capacity-achieving) schemes for this scenario require joint decoding of the multiple streams transmitted, entailing high computational complexity. In this paper, a low-complexity scheme requiring only single stream decoding is proposed. The scheme uses a matrix decomposition, which allows, by linear pre- and post-processing, to simultaneously transform both channel matrices to triangular forms, where the diagonal entries of both channels are equal. In conjunction with successive interference cancellation at each receiver, parallel channels are created, over each of which scalar coding and decoding may be used. We prove that this channel transformation conserves mutual information, and hence any sub-optimality of the proposed scheme is governed solely by the gap-to-capacity of the scalar coding scheme over the parallel channels.