VESA mount

Your best bet is to replace the computer wih a new 24" VESA mounted iMac. The reason I say this is 2012-2020 21.5 & 27" iMac stand is part of the main chassis, they cannot be disconnected unless you saw them off which is not recommended. In short, Apple does not not supply a retrofit VESA mount for iMacs made after 2011. So what does this leave you?:

• Search for third party solutions (they are all really hacks in my opinion).
• Replace the computer with a 2020 27" iMac that has a VESA mount built in or a 2021 24" iMac that has a VESA mount built in.

I'm sorry to say RUSD Tech is incorrect in this case. The kit he is recommending will NOT repeat will not work on your 2013 iMac.

The Apple VESA mounting kit works with 21.5" 27" ACD TBD and iMac Pro:

VESA Mount Adapter Kit for iMac and LED Cinema or Apple Thunderbolt Display - Education - Apple (IE)