Problem:
For how many values of is the least common multiple of the positive integers , and
Solution:
The prime factorizations of the given integers are
Because and are the only prime factors of the least common multiple of the three numbers, for some nonnegative integers and . In order for the least common multiple of , and to be must be , and can be any integer from to , inclusive. Thus there are acceptable values of .
The problems on this page are the property of the MAA's American Mathematics Competitions