There was a company called Seeburg that provided 16 rpm records and players to businesses for background music. They competed with Muzak. I have one of the records- it’s a bit wider than a regular 45 and has a larger hole in the middle. linky- Seeburg 1000 - Wikipedia
Lps were stamped out in a press. A blob of soft warm plastic was deposited on the die with a centre paper disc above and below. The press came down quite slowly, spreading the material over the ridges on the die which formed the groove on the surface. The operator used a knife to trim off the edge that would extrude from the machine before raising the top to release the now fully-formed, but still soft record. He would slip it into a paper sleeve and onto a rack before starting all over again. The whole process took over two minutes and a good operator would work two or three machines at a time.
The dies were etched from the original tapes and they were often stored for many years so that, if there was some renewed interest in the artist, more could easily be produced. This was usually after the artist died.
The decision to go for 1,2,3,4 or 1,3,2,4 would be made at the initial etching stage and dies were kept together in their pairs.