Asked by T315
Mark and Aki are building Hot Wheels tracks. Mark has 4-inch pieces to make his track, and Aki has 10-inch pieces to make his track. How long will their tracks be when they finish the same length?
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Answered by
GPT-4o mini
To find out when Mark and Aki's tracks will be the same length, we can use the least common multiple (LCM) of their track piece lengths.
Mark has 4-inch pieces, and Aki has 10-inch pieces. We need to find the LCM of 4 and 10.
1. **Prime factorization**:
- The prime factorization of 4 is \(2^2\).
- The prime factorization of 10 is \(2^1 \times 5^1\).
2. **Determining the LCM**:
- For the LCM, we take the highest power of each prime number that appears in the factorizations.
- For \(2\), the highest power is \(2^2\) (from 4).
- For \(5\), the highest power is \(5^1\) (from 10).
So, the LCM is calculated as:
\[
LCM = 2^2 \times 5^1 = 4 \times 5 = 20
\]
Therefore, the length of the tracks when they finish the same length will be **20 inches**.
Mark has 4-inch pieces, and Aki has 10-inch pieces. We need to find the LCM of 4 and 10.
1. **Prime factorization**:
- The prime factorization of 4 is \(2^2\).
- The prime factorization of 10 is \(2^1 \times 5^1\).
2. **Determining the LCM**:
- For the LCM, we take the highest power of each prime number that appears in the factorizations.
- For \(2\), the highest power is \(2^2\) (from 4).
- For \(5\), the highest power is \(5^1\) (from 10).
So, the LCM is calculated as:
\[
LCM = 2^2 \times 5^1 = 4 \times 5 = 20
\]
Therefore, the length of the tracks when they finish the same length will be **20 inches**.
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