There are lots of Kenmore canisters in that era, a great many diff. models and sometimes only a color change caused a different model number to be assigned. They've made Progressive models for some time, but they also offered other named models simultaneously, like the Whispertone (plain, 100, 200, 300). Plus entry level machines that simply said Kenmore with no model name. So, it might've been made right along with the Progressives.
A picture might help, but Kenmore schematics aren't in color to help with ID. Was the machine rectangular or oval-ish, that information might get us in the right decade.
If your object is to try to get another machine just like it, you may have to settle for something close but not necessarily the exact model number. Go to Google images and put in "Kenmore canister vacuum cleaner" or similar. You'll get to see lots of pictures and you might find something close. Also look up the same thing on eBay and check Craig's List in your area; lots of pictures there.
