Where are the LC_ locale global environment variables configured?

I want to change the language of my computer. I tried doing this with sudo dpkg-reconfigure locales. this changed the LANG environment variable in /etc/default/locale but none of the LC environment variables changed. /etc/default/locale says # File generated by update-locale so I presume there is some correct way of generating this file so that the LC variables are as desired. Oddly, after changing the LC_ variables by hand and sourcing /etc/default/locale when I rerun update-locale the LC variables inside /etc/default/locale keep their value rather than resetting to the old one. These also remain the same after a sudo dpkg-reconfigure locales. So may you are meant to just change these variables by hand and thereafter all the tools will keep them the same?