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? type your response into the box below.
To find out how many 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 factors of 9 are 3 * 3.
The prime factors of 12 are 2 * 2 * 3.
To find the LCM, we take the highest power of each prime factor:
2 * 2 * 3 * 3 = 36.
Therefore, it will take them 36 weeks to get paid at the same time.
To find out when Jiani and Rosa will get paid at the same time, we need to find the least common multiple (LCM) of 9 and 12, which represents the number of weeks it will take for both of their payment cycles to synchronize.
Step 1: Prime factorize the given numbers:
9 = 3^2
12 = 2^2 * 3
Step 2: Write down the highest power of each prime factor that appears in either of the factorizations:
Highest power of 2: 2^2
Highest power of 3: 3^2
Step 3: Calculate the LCM by multiplying the highest powers of each prime factor together:
LCM = (2^2) * (3^2) = 4 * 9 = 36
Therefore, it will take 36 weeks for Jiani and Rosa to get paid at the same time.
To find out how many weeks it will take for Jiani and Rosa to get paid at the same time, we need to determine the smallest common multiple of 9 and 12.
First, let's find the multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, ...
Next, let's find the multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, ...
From the lists above, we can see that the smallest number that appears in both lists is 36.
Therefore, it will take 36 weeks for Jiani and Rosa to get paid at the same time.