if a locally connected space has finite numbers of components then the space is finite or not?
i know that a compact locally connected space has finite numbers of components. but when the space is not compact still will it follow that it has finite components
Of course not. A component is a connected subspace and these can be as large as you like. A simple example: $X = [0,1]$ in the Euclidean topology has one component (i.e. it's connected), is locally connected and quite infinite.
It's true that a locally connected compact space $X$ has finitely many components (because these then form an open disjoint cover of $X$), but that's a very different thing from saying the space is finite.
A discrete space is locally connected and has as many components as it has points, so maybe you're confused with that?