Bottom of the grip.
The serial is probably on the bottom of the grip frame. Aftermarket grips can cover this number. If it was made after 1957, it should have a model number on the frame under the crane, under the rear of the barrel, like 19, or 19-1,2,3, etc. depending on revision. Otherwise if the number is K4539 in actuality, it should have been made in 1947, but my Jinks book says the first K frame 357 was made with ser. K260,003 in 1955. Therefore another look is in order? Might have a number before the letter in later guns. My book goes to 1976 on K frame guns.