"no such file to load -- zlib (LoadError)" while trying to install gems via rvm

On a fresh install of Ubuntu 10.04 LTS, I recently encountered the following error after installing "rvm":

no such file to load -- zlib (LoadError)

I ended up fixing this with:

sudo apt-get install zlib1g-dev \
  libssl-dev libreadline5-dev \
  libxml2-dev libsqlite3-dev

However, rvm appears to have a solution for this built-in. I haven't tried it, since I did the apt-get install above, but I have read that it worked for others:

rvm package install zlib