Euclid and the Large Synoptic Survey Telescope (LSST) are poised to dramatically change the astronomy landscape early in the next decade. The combination of high cadence, deep, wide-field optical photometry from LSST with high resolution, wide-field optical photometry and near-infrared photometry and spectroscopy from Euclid will be powerful for addressing a wide range of astrophysical questions. We explore Euclid/LSST synergy, ignoring the political issues associated with data access to focus on the scientific, technical, and financial benefits of coordination. We focus primarily on dark energy cosmology, but also discuss galaxy evolution, transient objects, solar system science, and galaxy cluster studies. We concentrate on synergies that require coordination in cadence or survey overlap, or would benefit from pixel-level co-processing that is beyond the scope of what is currently planned, rather than scientific programs that could be accomplished only at the catalog level without coordination in data processing or survey strategies. We provide two quantitative examples of scientific synergies: the decrease in photo-z errors (benefitting many science cases) when high resolution Euclid data are used for LSST photo-z determination, and the resulting increase in weak lensing signal-to-noise ratio from smaller photo-z errors. We briefly discuss other areas of coordination, including high performance computing resources and calibration data. Finally, we address concerns about the loss of independence and potential cross-checks between the two missions and potential consequences of not collaborating.
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