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Answer :
Final answer:
In 12 weeks, Jack, Art, Fran, and Megan will all be at the local kennel on the same day 7 times. This is determined by calculating the least common multiple (LCM) of their individual schedules and dividing the total days in 12 weeks by this LCM.
Explanation:
The question asks how many times in 12 weeks will all 4 volunteers at a local kennel be at the clinic on the same day based on their individual schedules. This is a least common multiple (LCM) problem. Let's calculate.
Jack works every 4 days
Art works every 6 days
Fran works every 2 days
Megan works every 3 days
To find when all four helpers will be at the clinic on the same day, we calculate the LCM of their schedules: 4, 6, 2, 3. The LCM of 4, 6, 2, 3 is 12. This means every 12 days, they all will work at the clinic on the same day. Now, 12 weeks equals 84 days (12 weeks × 7 days = 84 days). We divide 84 by the LCM, 12.
84 days ÷ 12 days/schedule = 7 times
Therefore, in 12 weeks, all four helpers will be at the clinic on the same day 7 times.
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All 4 helpers will be at the clinic on the same day 7 times in 12 weeks.
What is Prime Factorization?
"Prime Factorization" is the process of determining which prime numbers multiply together to get the original number.
To find the number of times in 12 weeks that all 4 helpers will be at the clinic on the same day, we need to find the least common multiple (LCM) of the numbers 4, 6, 2, and 3.
First, we can find the prime factorization of each number:
4 = 2 x 2
6 = 2 x 3
2 = 2
3 = 3
Next, we can find the LCM by taking the highest power of each prime factor that appears in the factorizations:
LCM = 2 x 2 x 3 = 12
Therefore, all 4 helpers will be at the clinic on the same day every 12 days. Since 12 weeks is equivalent to 84 days, we can divide 84 by 12 to get the number of times:
84 ÷ 12 = 7
So, all 4 helpers will be at the clinic on the same day 7 times in 12 weeks.
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