in HTML5, there is the form attribute. Basically
From @Voldemaras Birškys' answer, I've improved his script to work as a polyfill so you can still have the form attribute no your button and it will work as if EDGE/IE would respect the form attribute.
The main difference is that now we include form on the external submit button.
Also, inside the click handler I just use the event to get the target element and from id discover the id of the target form.
:)