This thread provides quite a bit of background:
https://www.vintage-radio.net/forum/...d.php?t=151267 “Why both 33 and 45?”
It is covered in that thread but in particular there was a full suite of mathematics and engineering behind RCA’s choice of 45 rev/min – a new speed at the time - and a 7-inch disc diameter. RCA did consider 33⅓ and 78.26 rev/min, and other disc sizes, but rejected both as being less suitable in relation to its objective, which was to produce a fast and reliable record-changing system.
Columbia chose the existing 33⅓ rev/min transcription speed for its LP. The readily available articles, such as that attached, do not explain why, although one may infer that the engineering analysis showed that there was no good reason not to do so. The full answer was probably provided in the article – which I have not seen - in the IRE Journal for 1949 August, available (for purchase) as an IEEE paper, at:
https://ieeexplore.ieee.org/document/1698116, “The Columbia Long-Playing Microgroove Recording System”, by P. Goldmark et al. Post facto support for the 33⅓ rev/min choice was provided by EMI in the WW article: Turntable Speeds – What is the Best Speed for Microgroove Recording?” by G.F. Dutton, attached to post #21 in the above-mentioned thread.
Cheers,