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From the Audacity page:
How do I download and install the LAME MP3 encoder?
Because of software patents, we cannot distribute MP3 encoding software ourselves. Follow these instructions to use the free LAME encoder to export MP3 files with Audacity.
Windows
1. Go to the
LAME download page.
2. Under "For Audacity 1.2.6 and 1.3.3 on Windows", left-click on the link "libmp3lame-win-3.97.zip" and save the zip folder to anywhere on your computer.
3. When you have finished downloading the ZIP folder, unzip it and save the file lame_enc.dll that it contains to anywhere on your computer.
4. The first time you use the "Export as MP3" command, Audacity will ask you where lame_enc.dll is saved.
5. In case of difficulty, please view our more detailed instructions at the Audacity Wiki.
Mac OS 9 or X
1. Go to the
LAME download page.
2. Download either libmp3lame or the version of LameLib for your operating system.
3. When you have finished downloading, use Stuffit Expander to extract the files. (This may happen automatically.)
4. Save the file called "LameLib" or libmp3lame.dylib anywhere on your computer.
5. The first time you use the "Export as MP3" command, Audacity will ask you where LameLib or libmp3lame.dylib is saved.