Question
When running together, Malik finishes a lap in 8 minutes, while Nicole finishes it in 10 minutes.
After how many minutes will Malik and Nicole meet again at the starting point?
After how many minutes will Malik and Nicole meet again at the starting point?
Answers
GPT-4o mini
To find out when Malik and Nicole will meet again at the starting point after running together, we need to determine the least common multiple (LCM) of their lap times.
Malik takes 8 minutes to complete a lap, and Nicole takes 10 minutes to complete a lap.
The LCM of two numbers can be calculated by finding the prime factorization and using the highest exponent of each prime factor.
1. **Factorization of the numbers:**
- \(8 = 2^3\)
- \(10 = 2^1 \times 5^1\)
2. **Taking the highest exponent of each prime factor:**
- For the prime \(2\), the highest power is \(2^3\) (from \(8\)).
- For the prime \(5\), the highest power is \(5^1\) (from \(10\)).
3. **Calculating the LCM:**
\[
\text{LCM} = 2^3 \times 5^1 = 8 \times 5 = 40
\]
So, Malik and Nicole will meet again at the starting point after **40 minutes**.
Malik takes 8 minutes to complete a lap, and Nicole takes 10 minutes to complete a lap.
The LCM of two numbers can be calculated by finding the prime factorization and using the highest exponent of each prime factor.
1. **Factorization of the numbers:**
- \(8 = 2^3\)
- \(10 = 2^1 \times 5^1\)
2. **Taking the highest exponent of each prime factor:**
- For the prime \(2\), the highest power is \(2^3\) (from \(8\)).
- For the prime \(5\), the highest power is \(5^1\) (from \(10\)).
3. **Calculating the LCM:**
\[
\text{LCM} = 2^3 \times 5^1 = 8 \times 5 = 40
\]
So, Malik and Nicole will meet again at the starting point after **40 minutes**.