2007 AMC 10B Problems/Problem 24
Problem
Let denote the smallest positive integer that is divisible by both and and whose base- representation consists of only 's and 's, with at least one of each. What are the last four digits of
Solution
For a number to be divisible by the last two digits have to be divisible by That means the last two digits of this integer must be
For a number to be divisible by the sum of all the digits must be divisible by The only way to make this happen is with 9 's. However, we also need one
The smallest integer that meets all these conditions is . The last four digits are
See Also
2007 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 23 |
Followed by Problem 25 | |
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