Final answer:
Frederick, Rockville, and Gaithersburg are all cities located in the state of Maryland, with Rockville and Gaithersburg in Montgomery County and Frederick in Frederick County.
Step-by-step explanation:
The state that includes Frederick, Rockville, and Gaithersburg is Maryland. These cities are located in the central part of the state, with Rockville and Gaithersburg being part of Montgomery County, and Frederick serving as the county seat of Frederick County.
Maryland is known for its significant history, proximity to Washington D.C., and its diverse geography ranging from sandy dunes in the east, pine groves in the Maryland mountains to the west, to urban areas like Baltimore and Annapolis.