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Location in Pennington County and the state of South Dakota. Box Elder, South Dakota. Box Elder (Lakota: ÄhaÅÅ¡ÃºÅ¡ka; box elder maple) is a city in Meade and Pennington counties in the State of South Dakota. The population was 7,800 at the 2010 census. Ellsworth Air Force Base lies on the north side of the city. Box Elder was named from nearby Boxelder Creek.
Brigham City is a city in Box Elder County, Utah, United States. The population was 17,899 at the 2010 census. It is the county seat of Box Elder County. It lies on the western slope of the Wellsville Mountains, a branch of the Wasatch Range at the western terminus of Box Elder Canyon.