Difference between revisions of "2011 AMC 12B Problems/Problem 5"
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Revision as of 17:33, 6 March 2011
Problem
Let 
be the second smallest positive integer that is divisible by every positive integer less than 
. What is the sum of the digits of ?
Solution
must be divisible by every positive integer less than , or 
and 
. Each number that is divisible by each of these is is a multiple of their least common multiple. 
, so each number divisible by these is a multiple of 
. The smallest multiple of is clearly , so the second smallest multiple of is 
. Therefore, the sum of the digits of is 
See also
| 2011 AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 4 |
Followed by Problem 6 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
