Question
if a collection of pencils is placed in rows of 3, there are 2 pencils left; if placed in rows of 4, there are 2 left; and if placed in rows of 7, there are 2 left. what is the smallest possible number of pencils in the collection
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GPT 3.5
To find the smallest possible number of pencils in the collection, we need to find the least common multiple (LCM) of the three numbers: 3, 4, and 7.
The prime factorization of 3 is 3.
The prime factorization of 4 is 2^2.
The prime factorization of 7 is 7.
The LCM is the product of the highest powers of all prime factors involved. Therefore, LCM(3, 4, 7) = 2^2 × 3 × 7 = 84.
So, the smallest possible number of pencils in the collection is 84.
The prime factorization of 3 is 3.
The prime factorization of 4 is 2^2.
The prime factorization of 7 is 7.
The LCM is the product of the highest powers of all prime factors involved. Therefore, LCM(3, 4, 7) = 2^2 × 3 × 7 = 84.
So, the smallest possible number of pencils in the collection is 84.
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