Will sigma 24 -70 DG HDM ex fit on Nikon d3100 and canon EOS 5D mark iii?

Will sigma 24 -70 DG HDM ex fit on Nikon d3100 and canon EOS 5D mark iii? - 1

NOPE

If you have a Nikon D3100, you need to buy the Sigma lens which has an onboard autofocus motor and has a Nikon mount

If you have a full frame Canon 5D, Mark III, then you need to buy a Sigma lens, again with an onboard auto-focus motor and has a Canon EF mount

The Sigma 24 -70 DG HDM EX has been discontinued, replaced by the 24-70mm F2.8 DG OS HSM | Art lens which costs about $1,300 and comes in either Nikon, Sigma or Canon mounts

I will not ask you how you ended up with two camera systems, but in time, you may want to do some research and see which system you want to adopt

At this time, the Nikon D850 is going to out perform any of the Canon 5D full frame cameras.

If the lens has a Nikon F mount, then it's going to fit onto the D3100, and it can be adapter to fit onto any Canon.
However, the lens would be manual focus on the D3100 since the D3100 doesn't have an AF motor (thanks Nikon). Even if it did and it had a Nikon F mount, you still would not have AF when used on a Canon with a Nikon to Canon adapter.

You can't put Canon lenses onto Nikons because Canon lenses require a shorter distance between the lens and sensor and Nikon bodies are thicker than Canon.

It will fit one or the other. Not both.
Sigma supply that lens to fit Canon OR Nikon. It can't be switched.

You mean one lens to fit both a Nikon and a Canon? No.

It's one or the other but NOT both. Look it up on the Internet, or call the Sigma company or one of its satellite shops.