In　this　paper,　we　introduce　the　lower-bounded　knapsack　median　problem　(LB　knapsack　median).　In　this　problem,　we　are　given　a　set　of　facilities,　a　set　of　clients,　a　budget　B　and　a　lower　bound　L.　Every　facility　is　associated　with　a　weight.　Every　facility-client　pair　is　associated　with　a　connection　cost.　The　aim　is　to　select　a　subset　of　facilities　to　open　and　connect　every　client　to　some　opened　facility,　such　that　the　total　weights　of　the　selected　facilities　is　no　more　than　B,　any　opened　facility　is　connected　by　at　least　L　clients　and　the　total　connection　costs　is　minimized.　As　our　main　contribution,　we　study　the　LB　knapsack　median　and　present　two　approximation　algorithms　with　ratios　of　2730　and　1608.　The　first　algorithm　is　based　on　reduction　and　the　improved　second　algorithm　is　based　on　an　intuitive　observation.　Additionally,　we　adapt　these　two　algorithms　to　the　lower-bounded　k-median　problem　(LB　k-median)　and　obtain　the　approximation　ratios　of　610　and　387.　©　2020,　Springer　Nature　Switzerland　AG.