Can My iMac be updated it runs MSOS High Sierra 10.13.6?

The Age of this computer will Govern what newer version of macOS it will Qualify to install. Use About this Mac from the Apple Icon on Desktop - the required Information will be there.

With the above information in-hand - follow this How to get old versions of macOS and verify what version this computer Qualifies to install.  For Best results use Safari to commence the download as Others may not work.

Safari will open a redirect and open the Apple Store where the download can commence.

If no ” Get Button “  Replace the https in the page's address to macappstore. Credit to Contributor @Niel

macOS High Sierra 10.13 hardware requirements

Make Time Machine Backup  is very useful and can be used to Revert to Previous Working macOS

Back up your data, check your applications for compatibility, and depending on which iMac model you have, click on Mojave, Catalina, Big Sur, or Monterey; it needs to be a 2012 or newer one to run a higher OS. If you get a Mac App Store preview page, change the https at the beginning of its address to macappstore.

Catalina and newer won't run 32-bit software; download and use Go64 to scan for it. To look up other programs, click here.

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