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2011 AMC 12B Problem 5

Problem 5 of 25EasierNumber Theory

Let NN be the second smallest positive integer that is divisible by every positive integer less than 7.7. What is the sum of the digits of N?N?

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Solution

A number divisible by every integer from 11 to 66 must be a multiple of lcm⁡(1,2,3,4,5,6)=60.\operatorname{lcm}(1,2,3,4,5,6)=60. The second smallest positive multiple of 6060 is 120,120, whose digit sum is 1+2+0=3.1+2+0=3. Thus, the correct answer is A.

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Concepts: least common multiple · digits

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.