There many different Facebook Like Box plugins available in free market. By default Facebook provides only fixed width like box widget code and there are very few plugins available that allows you to insert fluid Facebook like box widgets.
This tutorial is on new responsive Facebook like box plugin that allows you to add a mobile friendly fluid width Facebook like box with an easy to use widget and shortcode
Installation & Usage: Install and activate Faceboook Like Box Responsive then visit your admin area Dashboard -> Appearance -> Widgets page and drag its widget to your sidebar.
Now type your page name and click the ‘Save’ button. The widget allows you to show faces, stream and header.
In-case you need Facebook like box in a non-widgetized area then use the shortcode:
[fb-box id="117017735039638" pagename="marketertheme" show_faces="true" stream="false" header="false" border="false"]