Aims. Large-Sized Telescope 1 (LST-1), the prototype for the Large-Sized Telescope at the upcoming Cherenkov Telescope Array Observatory, is concluding its commissioning phase at the Observatorio del Roque de los Muchachos on the island of La Palma. The proximity of LST-1 to the two MAGIC (Major Atmospheric Gamma Imaging Cherenkov) telescopes makes it possible to carry out observations of the same gamma-ray events with both systems.|Methods. We describe the joint LST-1+MAGIC analysis pipeline and used simultaneous Crab Nebula observations and Monte Carlo simulations to assess the performance of the three-telescope system. The addition of the LST-1 telescope allows for the recovery of events in which one of the MAGIC images is too dim to survive analysis quality cuts.|Results. Thanks to the resulting increase in the collection area and stronger background rejection, we found a significant improvement in sensitivity, allowing for the detection of 30% weaker fluxes in the energy range between 200 GeV and 3 TeV. The spectrum of the Crab Nebula, reconstructed in the energy range between similar to 60 GeV and similar to 10 TeV, is in agreement with previous measurements.