When TechSpot tested G-SYNC monitors for compatibility they had great success, indeed any issues they found they decided were more likely issues with the display as opposed to compatibility issues.  LG noticed that they didn't test any of their displays and so they sent over a few for review, which TechSpot happily accepted.  The 32GK850F, 24GL600F, 27GK750F, 32GK650F and 34GK950F were all tested and found to be fully compatible, if you happen to have one.

If you are not familiar with that third model, it is a rare 27" 1080p TN display with a top refresh rate of 240Hz, maybe not the prettiest but certainly one of the fastest 27 inchers around. 

"Earlier this year we first put Nvidia's support for FreeSync monitors to the test, grabbed every FreeSync monitor we had in the office, and verified that in all cases adaptive sync worked as expected. LG recently sent us 5 of their latest FreeSync monitors, which we've used to revisit Nvidia's FreeSync support."

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Displays