It would probably not have been practical to do a three-stage, single launch LOR Saturn/Apollo all on kerosene; the specific impulse advantage of the J-2 engines is just too great.
According to my spreadsheet estimates, a four-stage kerosene rocket almost 3 times the size of Saturn V could do it.
The translunar stage, S-IV-K, is 127138 tons propellant, 812 tons dry, 47 tons payload (Apollo CSM and LM). 1x H-1 engine (as used on the Saturn 1B).
Third stage, S-III-K, 423t465 propellant, 27t35t dry, 1x F-1 engine.
Second stage, S-II-K, 1504t1674t propellant, 96t126t dry, 3x F-1 engines.
First stage, S-I-K, 5640t6392t propellant, 360t408t dry, 14x16x F-1 engines.
All-up mission launch mass of this "Saturn XIV"XVI" would be 82329297 tons.
First 3 stages produce ~9600 m/s of delta-v, taking the beast to a 185km circular orbit. Fourth stage produces ~3400 m/s to send the spacecraft to the moon.
The mass could be brought down substantially withwith more optimized engines; both the F-1 and H-1 were designed as first-stage engines. Larger nozzle extensions, particularly on the 3rd and 4th stages, would improve the specific impulse, without requiring all-new engine designs. With an "H-1V" producing 320s ISP and an "F-1V" producing 337s, total launch mass could be brought down to 62706820 tons or so, with "only" 1112 engines on the first stage.
Both my answers are, obviously, merely rough Kerbal-style feasibility estimates.
(Amended tonnages to reflect more conservative fuel tank mass fractions.)