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Answer :
To solve the problem of determining when Caylan will first remove the scones, muffins, and cookies from the oven at the same time, we need to find a common time when all three will be finished baking simultaneously. This can be done by finding the least common multiple (LCM) of the baking times for the three items.
1. Understand the Baking Times:
- Scones take 15 minutes to bake.
- Muffins take 12 minutes to bake.
- Cookies take 10 minutes to bake.
2. Identify the Problem:
We want to determine the earliest time when all three types of baked goods can be removed from the oven together. This requires finding the smallest number that is a multiple of each of the baking times: 15, 12, and 10.
3. Find the Least Common Multiple (LCM):
- The LCM of several numbers is the smallest number that all of them divide into without leaving a remainder.
- For our problem, we need to calculate the LCM of 15, 12, and 10.
4. Calculation of LCM:
- Prime Factorization:
- 15 = 3 × 5
- 12 = 2² × 3
- 10 = 2 × 5
- Combine Prime Factors:
To find the LCM, take the highest power of each prime number appearing in any factorization:
- Highest power of 2 is 2².
- Highest power of 3 is 3.
- Highest power of 5 is 5.
- LCM = 2² × 3 × 5 = 4 × 3 × 5 = 60
5. Conclusion:
Therefore, the earliest time when Caylan can remove all the trays simultaneously is after 60 minutes. This is when the scones, muffins, and cookies will all have completed a full baking cycle at the same time. So, Caylan will first remove the trays at the same time 60 minutes after starting.
1. Understand the Baking Times:
- Scones take 15 minutes to bake.
- Muffins take 12 minutes to bake.
- Cookies take 10 minutes to bake.
2. Identify the Problem:
We want to determine the earliest time when all three types of baked goods can be removed from the oven together. This requires finding the smallest number that is a multiple of each of the baking times: 15, 12, and 10.
3. Find the Least Common Multiple (LCM):
- The LCM of several numbers is the smallest number that all of them divide into without leaving a remainder.
- For our problem, we need to calculate the LCM of 15, 12, and 10.
4. Calculation of LCM:
- Prime Factorization:
- 15 = 3 × 5
- 12 = 2² × 3
- 10 = 2 × 5
- Combine Prime Factors:
To find the LCM, take the highest power of each prime number appearing in any factorization:
- Highest power of 2 is 2².
- Highest power of 3 is 3.
- Highest power of 5 is 5.
- LCM = 2² × 3 × 5 = 4 × 3 × 5 = 60
5. Conclusion:
Therefore, the earliest time when Caylan can remove all the trays simultaneously is after 60 minutes. This is when the scones, muffins, and cookies will all have completed a full baking cycle at the same time. So, Caylan will first remove the trays at the same time 60 minutes after starting.
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