The 1960 Kenmore models were still using the more "rounded" cabinet style. The squared-off cabinet was introduced in '61, but this dryer has a different control panel than the '61 LK. I believe this dryer may be a '64.
This dryer is definitely later than 1960, in 1961 they went to the setup with using a separate belt for the fan and had a belt going around the drum just like in today’s current 29” top filter dryers.
This is the rare electronically controlled 1964 dryer that did not come out till the 1965 LKMs came out and introduced electronic dryness control.
Sears built this dryer for all the people that bought 1964 LKM washers but did not buy a dryer, this gave thhse customers a chance to ge the latest and most advanced KM dryer to match their washer.