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Answer :
To find out how many minutes after Caylan puts the trays in the oven he will first remove the scones, muffins, and cookies at the same time, we need to determine the least common multiple (LCM) of the baking times for each of the baked goods.
Here's how you can find the LCM step-by-step:
1. Identify the baking times:
- Scones bake for 15 minutes.
- Muffins bake for 12 minutes.
- Cookies bake for 10 minutes.
2. Find the LCM of the three numbers (15, 12, and 10):
- Prime factorize each number:
- 15 = 3 × 5
- 12 = 2² × 3
- 10 = 2 × 5
- List all prime factors, taking the highest power of each present in the factorizations:
- For prime number 2, the highest power is 2² (from 12).
- For prime number 3, the highest power is 3¹ (from both 15 and 12).
- For prime number 5, the highest power is 5¹ (from both 15 and 10).
- Multiply these together to get the LCM:
[tex]\[
LCM = 2² × 3 × 5 = 4 × 3 × 5 = 60
\][/tex]
So, the least common multiple of 15, 12, and 10 is 60.
Therefore, Caylan will first remove all three trays of scones, muffins, and cookies at the same time after 60 minutes.
Here's how you can find the LCM step-by-step:
1. Identify the baking times:
- Scones bake for 15 minutes.
- Muffins bake for 12 minutes.
- Cookies bake for 10 minutes.
2. Find the LCM of the three numbers (15, 12, and 10):
- Prime factorize each number:
- 15 = 3 × 5
- 12 = 2² × 3
- 10 = 2 × 5
- List all prime factors, taking the highest power of each present in the factorizations:
- For prime number 2, the highest power is 2² (from 12).
- For prime number 3, the highest power is 3¹ (from both 15 and 12).
- For prime number 5, the highest power is 5¹ (from both 15 and 10).
- Multiply these together to get the LCM:
[tex]\[
LCM = 2² × 3 × 5 = 4 × 3 × 5 = 60
\][/tex]
So, the least common multiple of 15, 12, and 10 is 60.
Therefore, Caylan will first remove all three trays of scones, muffins, and cookies at the same time after 60 minutes.
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Rewritten by : Jeany
