True linoleum is linseed oil, sawdust and canvas.

As for "vinyl asbestos" tile, which was squares of glue-down, just don't grind it up and inhale it, don't sand it. If you soften the flooring with heat and scrape it off, it'slow hazard.

Those people who got cancer from asbestos had several things in common: Heavy smoking for years and HEAVY asbestos exposure (worked spraying it as insulation, mining it or making things of it).

FYI, there is more asbestos in the air in the San Jose area naturally than the EPA permits on a job site.

The adhesive that was used for floor covering applications during that period is, "cutback" and contains asbestos fibers as a binder.
There is a simple test that you can do to ascertain the presents of cutback adhesive.
Using a sharp blade cut a 2"x2" square through one or both layers of the flooring material and remove the first layer,
The exposed adhesive may be black in color.
Heat some water to boiling and spill a few drops on the adhesive.
Repeat for each layer.
If the water drops remain intact, the adhesive is cutback.
If the adhesive dissolves and liquifies, you do not have cutback adhesive.
Asbestos becomes dangerous and absorbable when it is "friable", IE. airborne.
There are a number of citrus based removers which can be safely used.

See Inspectapedia for authoritative references to asbestos identification, remediation and removal.