Which form is correct?
None of A,B or C divides X
None of A,B and C divides X
I would use:
None of A,B or C divides X.
because with some values you might be able to say:
Some of A,B or C divide X.
in which case you need or because it is not all or nothing.
Also "A,B and C" implies they exist as a fixed set, which is not known without any context.