To find the smallest number of crackers that Jill can pack, we need to determine the least common multiple (LCM) of the two group sizes: 6 (for pretzels) and 9 (for crackers).
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Find the prime factorization of each number:
- The prime factorization of \(6\) is \(2 \times 3\).
- The prime factorization of \(9\) is \(3^2\).
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Identify the highest power of each prime factor present in either number:
- The prime \(2\) appears in \(6\) as \(2^1\).
- The prime \(3\) appears in \(6\) as \(3^1\) and in \(9\) as \(3^2\).
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Combine the highest powers:
- For \(2\), the highest power is \(2^1\).
- For \(3\), the highest power is \(3^2\).
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Calculate the LCM: \[ \text{LCM} = 2^1 \times 3^2 = 2 \times 9 = 18 \]
The LCM of 6 and 9 is 18, which means the smallest number of crackers that Jill can pack (while also packing an equal quantity of pretzels) is \(\boxed{18}\).