My iMac (late 2012) started running very slow: beach ball turning on every click for up to 5 minutes and some programs do not respond. Ran virus chec and CleanMyMac (latest version) but no change. Then ran disk repair but it appears not to help.

It sounds like you may have a failing hard drive. Make a good backup now.

Uninstall the anti-virus and CleanMyMac as per the developer's instructions. No Anti-Virus software or so-called “cleaning” apps are needed or recommended for Mac OS. They can conflict with Mac's own built-in security. At best they will slow your Mac by using unnecessary resources and at worst will bork your entire system. Your Mac has all the built-in protection you need.

https://www.apple.com/macos/security/

Then you can try running Etrecheck. It is a diagnostic tool that's very useful to us in finding problems. Also it will give us further specs on your Mac. After it runs post the log file here. It will contain no personal information. 

To post the log file click on share report and use the Additional Text icon in your reply window.

Are you sure you have an up to date hard drive? Your hard drive might be dying.

The most common problems of a failing hard drive are, slow interface (what you said), failing to restart or boot up, missing files, and much more.

Make a backup quick, because it might be too late before you lose all of your work.

Second, uninstall Anti-Virus and CleanMyMac. These applications can interfere with your disk and completely ruin the efficiency of your system.

Third, erasing files won’t work. They just go to your trash bin which is part of your hard drive.

Best Regards,

mdp1101

Etrecheck is not reporting a failing hard drive, but your runtime is very bad. Still I would suspect the hard drive. Also you still have remnants of CMM in the below file paths, which Etrecheck is reporting as affecting system performance.

Launch Daemons:
  [Loaded] com.macpaw.CleanMyMac3.Agent.plist (? 7f4ba9a8  - installed 2015-10-05)
Unsigned Files:
  Launchd: /Library/LaunchDaemons/com.macpaw.CleanMyMac3.Agent.plist
    Executable: /Library/PrivilegedHelperTools/com.macpaw.CleanMyMac3.Agent

Try running the free DriveDx. It's a more robust utility for checking the health of your hard drive. It will not make any repairs just check and report. You can post the output here.

https://binaryfruit.com/drivedx

macjack wrote:

Try running the free DriveDx.

Just to clarify one thing, DriveDx has a free trial period but once expired it will no longer run without purchase.

It looks OK. I'm not sure what else may be causing the issues. A real test would be installing a system onto an external drive and testing with the clean install.

OK, that's good news!