We consider transmission of two arbitrarily correlated sources over a discrete memoryless asymmetric multiple access channel, where one of the sources is available at both transmitters. We want to transmit the common source lossless in the Shannon sense, while there is a distortion requirement on the other source. For a given bandwidth ratio between the channel and source bandwidths and a distortion requirement, we derive the necessary and sufficient conditions, and show that separation of source and channel coding is optimal. Finally, we extend our results to the case where perfect casual feedback is available at either one or both of the transmitters.