  Strong lensing by galaxy clusters can be used to significantly expand the
survey reach, thus allowing observation of magnified high-redshift supernovae
that otherwise would remain undetected. Strong lensing can also provide
multiple images of the galaxies that lie behind the clusters. Detection of
strongly lensed Type Ia supernovae (SNe Ia) is especially useful because of
their standardizable brightness, as they can be used to improve either cluster
lensing models or independent measurements of cosmological parameters. The
cosmological parameter, the Hubble constant, is of particular interest given
the discrepancy regarding its value from measurements with different
approaches. Here, we explore the feasibility of the Vera C. Rubin Observatory
Legacy Survey of Space and Time (LSST) of detecting strongly lensed SNe in the
field of five galaxy clusters (Abell 1689 and Hubble Frontier Fields clusters)
that have well-studied lensing models. Considering the 88 systems composed of
268 individual multiple images in the five cluster fields, we find that the
LSST will be sensitive to SNe~Ia (SNe~IIP) exploding in 41 (23) galaxy images.
The range of redshift of these galaxies is between $1.01 < z < 3.05$. During
its 10 years of operation, LSST is expected to detect $0.2\pm0.1$ SN~Ia and
$0.9\pm0.3$ core collapse SNe. However, as LSST will observe many more massive
galaxy clusters, it is likely that the expectations are higher. We stress the
importance of having an additional observing program for photometric and
spectroscopic follow-up of the strongly lensed SNe detected by LSST.
