Although this technology has been prevalent in higher ed for many years, K-12 is only recently reviewing its features in consideration of some of the more advanced pedagogical strategies like flipped learning. Below is a list of the providers that have been making some headway with K-12 schools. These are all free to try. Some have site license requirements for an entire class and some are completely free (but remember there could be some privacy issues related to those).
CK-12 (free and provides limited curriculum)
Canvas (free trial-limited cost enterprise license)
CourseSites (Blackboard's limited demo version)
Edmodo (facebook-like interface; free)facebook-like interface; free)
Google Classroom (must be a Google Apps for Education User)
Schoology (basic package is free; enterprise cost for an entire system)
*The LMS market fluctuates constantly. These are some of the more well-known systems, but there are hundreds that serve similar functions. You'll want to explore this further if you plan to use it regularly in your classroom or serve on a technology committee to make these decisions.