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Jiani gets paid for a job every 9 weeks and Rosa gets paid for a job every 12 weeks. How many weeks will it take for them to ge...Question
Jiani gets paid for a job every 9
weeks and Rosa gets paid for a job
every 12 weeks. How many weeks
will it take for them to get paid at the
same time?
weeks and Rosa gets paid for a job
every 12 weeks. How many weeks
will it take for them to get paid at the
same time?
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To find out when Jiani and Rosa will get paid at the same time, we need to determine the least common multiple (LCM) of their pay periods: 9 weeks and 12 weeks.
1. **Find the prime factorization of each number:**
- 9: \(3^2\)
- 12: \(2^2 \times 3^1\)
2. **Identify the highest power of each prime:**
- For the prime number 2, the highest power is \(2^2\) (from 12).
- For the prime number 3, the highest power is \(3^2\) (from 9).
3. **Multiply these together to get the LCM:**
\[
LCM = 2^2 \times 3^2 = 4 \times 9 = 36
\]
Thus, Jiani and Rosa will both get paid at the same time in **36 weeks**.
1. **Find the prime factorization of each number:**
- 9: \(3^2\)
- 12: \(2^2 \times 3^1\)
2. **Identify the highest power of each prime:**
- For the prime number 2, the highest power is \(2^2\) (from 12).
- For the prime number 3, the highest power is \(3^2\) (from 9).
3. **Multiply these together to get the LCM:**
\[
LCM = 2^2 \times 3^2 = 4 \times 9 = 36
\]
Thus, Jiani and Rosa will both get paid at the same time in **36 weeks**.
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