is clean my max X legitimate?

No. It's utter garbage. Almost malware itself.

Never install any app that claims to clean, optimize or speed up your Mac. That includes all AV software, which are all 100% useless. The one and only exception to the latter is MalwareBytes for Mac. Its main purpose is to try and clean up any malware and adware you've already installed. Not try to prevent it. It's free to use and easily uninstalled from its menu option when you're done with it.

A real app? yes. Needed? Absolutely not! Run Away!

Macs—cat-like—have cleaned themselves since the intro of OSX over 20 years ago. Elegant, automated self-maintenance routines run in the wee hours of the morning and take care of all housekeeping needs. Apple's built-in systems even defrags if needed.

Adding third-party dreckware like CMM and anything else that claims to clean, optimize, tune up, etc are thus useless and will extract a performance penalty. Several reports showing hard data for disk drive performance posted here over the last few years show a 20-40% IMPROVEMENT in a drive's write/read speeds when CMM was removed.

You paid Apple good money to built amazing self-maintenance into the macOS. Please let your Mac be a Mac.

The Application is " legitimate " but the user best check out the Issues this Specific Application can and will do to the computer.

On these Forums , " CleanMyMac " is sometimes known as " BrickMyMac "

The inference is plain - stay way from it even if you see it available on the Apple Apps Store, which it is.

Before you ask how can Apple Allow this Developer to sell on the Apple Apps Store

Certain Applications maybe available on the Apple Apps Store - this only means the Developer is prepared to pay Apple a portion on each sale. What the Application may do to the computer is up to the User to check this out before purchase

Sorry, forgot the link and read some of the first 600 posting

Arrive at you own conclusions

This will include CleanMyMac

EDITED

I'll add my voice to the chorus:

Never install any app that claims to "tune up", "speed up" or "clean up" your Mac. These apps exist for one reason: to separate the unwary and inexperienced user from their hard-earned money. At best they do very little, at worst, they can damage your OS installation and cause far more problems than they "solve".

No, all that this programs are doing is making your Mac slower, and they weaken macOS built in security so your Mac comes more prone to malware. Don't use this kind of software on your Mac.

I suppose that depends on what you mean by "legitimate".

If you mean does it perform a useful function without causing undue harm, then no, it's not. I concur with all the other responses.

You may also what to look at this:

Effective defenses against malware and ot… - Apple Community

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