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? Type your response into the box below.(1 point)
The number of weeks it will take for them to get paid at the same time is the least common multiple (LCM) of 9 and 12.
The prime factors of 9 are 3 and 3.
The prime factors of 12 are 2, 2, and 3.
The LCM is the product of the highest powers of all prime factors, which gives us LCM = 2 × 2 × 3 × 3 = 36.
Therefore, it will take 36 weeks for Jiani and Rosa to get paid at the same time.
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 LCM is the smallest number that is divisible by both 9 and 12.
To find the LCM, we can find the prime factors of both numbers and then multiply the highest powers of each factor.
Prime factors of 9: 3 * 3
Prime factors of 12: 2 * 2 * 3
To find the LCM, we multiply the highest powers of each factor:
2 * 2 * 3 * 3 = 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 find the least common multiple (LCM) of 9 and 12. The LCM is the smallest number that both 9 and 12 divide into evenly.
To find the LCM, we can use the prime factorization method. We will break down each number into its prime factors:
9 = 3 * 3
12 = 2 * 2 * 3
The LCM is found by multiplying all the prime factors with their highest exponent:
LCM = 2 * 2 * 3 * 3 = 36
So, it will take 36 weeks for Jiani and Rosa to get paid at the same time.