Problem:
Let be the set of the smallest positive multiples of , and let be the set of the smallest positive multiples of . How many elements are common to and ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The sets and consist, respectively, of the positive multiples of that do not exceed and the positive multiples of that do not exceed . Thus , the set of numbers that are common to and to , consists of the positive multiples of that do not exceed . Let represent the largest integer that is less than or equal to . Then the number of elements in the set is
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions