More than 100 people from institutions around the world participated in a virtual workshop, "Supporting Computational Science with Rubin LSST," on March 21-22, 2023. The workshop welcomed anyone involved in the process of turning LSST data into science, especially those requiring specific computational hardware or software. The meeting focused on science use cases with Rubin LSST, and how these might be paired with specific In-Kind contributed computing resources (Independent Data Access Centers and Scientific Processing Centers (IDACs and SPCs). The workshop was followed by a two-day technical discussion between members of the Rubin IDACs Coordination Group and Rubin Data Management, aimed at understanding how to meet the demand from the community use cases and identifying technical challenges. In this report, we summarize the outcome of the scientific workshop and the technical discussion, and identify some of the next steps needed for continuing progress.