A package of hotdogs usually contains 10 hot dogs and a package of buns usually contains 12 buns. How many packages of hotdogs and buns should a person but to be sure that there are equal numbers of each?

The least common multiple of 10 and 12 is 60.

60 sandwiches is the least number that can be built

with integer-multiples of packaged dogs and buns.

(10 dogs/package) x (6 packages) = 60 dogs

(12 buns/package) x (5 packages) = 60 buns