Problem:
Let be the second smallest positive integer that is divisible by every positive integer less than 7 . What is the sum of the digits of ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Because is divisible by 3,4 , and 5 , the prime factorization of must contain one 3 , two , and one 5 . Furthermore is divisible by every integer less than 7. Therefore the numbers with this property are precisely the positive multiples of 60 . The second smallest positive multiple of 60 is 120 , and the sum of its digits is .
The problems on this page are the property of the MAA's American Mathematics Competitions