Install Latest LibreOffice Version

On Ubuntu 12.04 LibreOffice is outdated and you are only getting updates for 3.7.x version.
Current latest version of LibreOffice is 4.x. Version 4 brings new features Ubuntu global menu integration and better support for MS Office files formats.

You have few options for updating LibreOffice.

Bleeding edge PPA

This PPA have dailly builds of LibreOffice and it is recommended only for users who want's to test new features. This is not stable version and it's not recommended to use this PPA on production machine.

sudo apt-add-repository ppa:libreoffice/ppa && sudo apt-get update && sudo apt-get upgrade 

4.1.x PPA

This PPA provides version 4.1.x (currently latest) of LibreOffice and updates. You need to keep in mid when version 4.2.x is released this PPA will not provide upgrade to version 4.2.x

sudo apt-add-repository ppa:libreoffice/libreoffice-4-1 && sudo apt-get update && sudo apt-get upgrade 

There is also PPA for 4.0.x and older version 3.6, 3.5 and 3.4

Direct update

You can also manually download latest version of LibreOffice