Final answer:
The lowest taxonomic category shared by beetles and cicadas is the Class Insecta, which encompasses a wide range of insects and is part of the subclass Hexapoda.
Step-by-step explanation:
The lowest taxonomic category shared by both beetles and cicadas is the Class Insecta. Both beetles and cicadas fall under the subclass Hexapoda, which has an immense variety of species, including everyday insects such as ants, butterflies, and flies. They all exhibit different developmental processes such as complete or incomplete metamorphosis. In terms of hierarchy, the class is a higher category that groups organisms with similar characteristics, and since both beetles and cicadas are insects, they are part of the Class Insecta.