Divisibility into Paperclip Piles

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A total number of paperclips can be divided into 24 smaller piles of an equal number of clips each or 30 smaller piles of an equal number of clips each. What is the lowest possible total number of paperclips?

Review: Divisibility into Paperclip Piles


Explanation

The total number of paperclips is divisible by 24 and by 30. To find the smallest such number, we can find the prime factorizations of 24 and 30, by dividing them into factors until we can divide no further. We have and . Our total number must therefore have at least three 2's, one 3, and one 5. The smallest possibility is .

The correct answer is (C).


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