update current Mac
How can I update my Mac?
27 in late 2013
iMac Line (2012 and Later)
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An iMac 27” late 2013 can upgrade as far as Catalina macOS 10.15, and no further.
Back up, use (only) Safari to download the Mojave or Catalina installer from Apple, and upgrade. The pre-upgrade backup is the means to revert and recover, should there be a problem with the upgrade, or should some important app cease ro function.
If you upgrade to Catalina, all of your apps must be 64-bit. Existing 32-bit apps must be updated, upgraded, replaced, or retired. Use Go64 to find problem apps. This includes Microsoft Office 2011 and earlier, which will not work on Catalina and later.
Mojave macOS 10.14 is the last version that can run 32-bit apps, with the older interfaces.
Details and download links: How to get old versions of macOS - Apple Support
