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?(1 point)

Question

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Answer 1

To find the number of weeks it will take for Jiani and Rosa to get paid at the same time, we need to find the least common multiple (LCM) of 9 and 12.

The prime factorization of 9 is 3*3.
The prime factorization of 12 is 2*2*3.

To find the LCM, we take the highest power of each prime factor that appears in either number:
- The highest power of 2 that appears is 2*2 = 4.
- The highest power of 3 that appears is 3*3 = 9.

Therefore, the LCM of 9 and 12 is 4*9 = 36.

So, it will take 36 weeks for Jiani and Rosa to get paid at the same time. Answer: \boxed{36}.