  Hints of violation of lepton flavor universality in semileptonic $B$ decays
have prompted a renewed interest in leptoquarks at the low TeV scale. Among the
different scenarios suggested, some happen to violate also lepton number, yet
not much attention has been paid to the expected size of the associated lepton
number violating processes. In this note we examine this issue. We find that
there is a single leptoquark scenario compatible with the current size of the
anomalies which also violates lepton number. In this scenario (Majorana)
neutrino masses are radiatively generated. With the leptoquark parameters
extracted from fitting the flavor anomalies, one actually gets the right order
of magnitude for neutrino masses. We examine the associated effective field
theories both at the electroweak scale and at the hadronic scale and estimate
the size of the most relevant lepton number violating processes.
