Can we build and run asp.net core application without sdk ?

You can not build the application without SDK. You will not reach till there because to crate a project of type .NET Core x.x, you will need that SDK installed, If you are creating project by yourself. However, The application can be run in any machine without installing SDK if you publish the application self-contained mode. Otherwise, To run application as well, you might have to install Hosting Bundle or Runtime version of .NET Core.