Well I had a heck of a time getting the linoleum glue off of our townhouse's kitchen concrete slab. It took a while for me to get into a nice pattern, and then it was done.
It is about 102 sq. ft. and I started with a pair of pliers and various knives and pulled the linoleum up. This left a lot of glue on the floor on about half of the room, with many large spots with the paper backing from the PVC floor still attached.
I started with a 3" putty knife and scraped up what I could. A propane torch didn't do very well, but it did help where the glue had "squished" over to the side during application and was extremely thick. That part was wet, heat, scrape, sand, scrape, brush.
The glue seems to have some property that it would spread very quickly through water i.e. using a sponge and bucket, if your source becomes contaminated, you would reach the saturation level very quickly.
Wearing a mask and goggles, I got out the belt sander with 36 grit extra coarse belts and started ripping away. This resulted in taking about 3 belts to clear 3 sq. in. of floor. Towards the end it was most expeditious to slop about 3' around of CLEAN water on the floor to about a 1/8" depth and then spread and soak the glue matter and promptly wet sand it in a circluar pattern.
The glue matter was damp and neither stuck badly to the belt nor made too too much dust. Of course, you have to work with the material to get a feel for it. Spreading it in a semicircle prevented the accumulation of the glue in one place.
Then I alternated amongst the putty knife and a plastic dustmop and bin to scrape the larger clumps up. This minimized impact to the floor. That 36 grit will go right into the concrete. It also kept the sander belt relatively free of glue. Then a few times over the floor with a wet mop -- I left the sink running and just washed out the mop every time -- and it seems pretty clean and ready.
Of concern is that we have a large crack that runs along the corner of the floor and the outer wall (we are the end unit in a "double quad" config) for about 10 ft., and which runs out about 8" towards the center of the kitchen, about half way into the crack and almost practically perpendicular to it.
We have never had a flood so I think we have structural issues, but anyway...
The question is how to patch the concrete, is it necessary?