2011 AMC 12B Problem 5

Attempt Problem 5 of the 2011 AMC 12B below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2011 AMC 12B solutions, or check the answer key.

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5.

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?

33

44

55

66

99

Answer: A
Concepts:least common multipledigits
Difficulty rating: 990
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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