Graham Daniels
09/20/2024 · Elementary School
13. Higher Order The she puts her rocks into collection. When there are no rocks left over. 2 equal piles, therer rocks into 3 equal When she puts her piles, there are still no rocks left over. When she puts her rocks into 4 equal piles, there are still no rocks left over.
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It seems like you're describing a problem related to finding a number of rocks that can be evenly divided into 2, 3, and 4 equal piles. This is a classic problem in number theory, often related to finding the least common multiple (LCM) of the numbers involved.
To find a number that can be divided evenly by 2, 3, and 4, we need to determine the LCM of these numbers.
1. **Factors of each number**:
- 2 = \(2^1\)
- 3 = \(3^1\)
- 4 = \(2^2\)
2. **Determine the LCM**:
- The LCM is found by taking the highest power of each prime factor that appears in the factorization of the numbers.
- For 2, the highest power is \(2^2\) (from 4).
- For 3, the highest power is \(3^1\) (from 3).
3. **Calculate the LCM**:
\[
\text{LCM} = 2^2 \times 3^1 = 4 \times 3 = 12
\]
Thus, the smallest number of rocks that can be evenly divided into 2, 3, and 4 equal piles is **12**.
If you have any further questions or need additional assistance, feel free to ask!
Quick Answer
The smallest number of rocks that can be evenly divided into 2, 3, and 4 piles is 12.
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