Building .net framework 4.5 project with target framework 1.1 (Backwards compatibility issue)

Question

I am working on a mature project that was initially implemented with .net framework 1.1 .

By the time of progress, most of the modules have been upgraded or rewritten with .net framework 4.0 and 4.5.

Currently there are 3 asp .net web applications of the project.

1. Is running with framework 1.1
2. Is running with framework 4.0
3. Is running with framework 4.5

And I have a Visual Studio project, named as "CommonLibrary", written with framework 4.5

Is it possible to use my CommonLibrary in all projects by building it with proper target framework versions?