The Anglo-American typewriter pitches of Pica (10 characters per inch) and Elite (12 cpi) have as their common factor 1/60 of an inch.
An Anglo-American printer's point is approximately 1/72", and so a laser printer with a resolution of 360 dots per inch can produce Pica and Elite typewritten pages and also handle printer's points except for the small discrepancy for scale.
Autologic made a laser printer for typesetting use which, instead of having a resolution of 720 dpi, had one of 723 dpi, thus reflecting the fact that a printer's point is actually slightly smaller than 1/72".
But how about the Didot point? The "metric Didot point" of 0.375 millimetres can be harmonized well with the Continental typewriter pitches of 2.5 mm and 2.0 mm. All of these are multiples of 0.125 millimetre, and thus a resolution of 8 dots per millimetre allows these sizes to be matched.
In fact, they harmonize too easily; that is 203.2 dpi, too coarse for quality laser printing. So we can start with a minimum resolution of 406.4 dpi, and remember that in addition to integral multiples for higher resolution, we can also do half-integer multiples (such as 1.5 times the resolution, or 610.2 dpi or 24 dots per millimetre).
If we want the exact printer's point of 0.013837", we can go from 360 dpi to 361.35 dpi for a very close approximation.
Similarly, if we want the 1879 Berthold Didot point of 0.37593985 mm, we can go from 406.4 dpi to 405.384 dpi for a very close approximation.