Jiani gets paid for a job every 9

Question

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?

Answer 1

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.