Thank you for visiting Practice GCF and LCM Quiz Level F Caylan is making baked goods for a charity bake sale He places a tray of scones a tray. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
To determine when Caylan will first remove the scones, muffins, and cookies from the oven at the same time, we need to find the least common multiple (LCM) of the baking times for each item.
Here's how we do it step-by-step:
1. Identify the Baking Times:
- Scones take 15 minutes to bake.
- Muffins take 12 minutes to bake.
- Cookies take 10 minutes to bake.
2. Understand the Problem:
- We need to find a moment in time that is a multiple of each of these individual times (15, 12, and 10 minutes). This means we want the smallest number that all three of these numbers divide into without leaving a remainder.
3. Find the Least Common Multiple (LCM):
- The LCM of a set of numbers is the smallest positive integer that is divisible by all of the numbers in the set.
4. Calculate the LCM:
- Consider the prime factorizations:
- 15 = 3 × 5
- 12 = 2² × 3
- 10 = 2 × 5
- For the LCM, take the highest power of each prime number that appears in any factorization:
- Take 2² (from 12)
- Take 3 (from both 15 and 12)
- Take 5 (from both 15 and 10)
- Multiply these together: [tex]\(2² \times 3 \times 5 = 4 \times 3 \times 5 = 60\)[/tex].
5. Conclusion:
- The least common multiple of 15, 12, and 10 is 60. So, after 60 minutes, Caylan will first be able to remove the scones, muffins, and cookies from the oven at the same time.
Therefore, the answer is that Caylan will first remove all the trays at the same time after 60 minutes.
Here's how we do it step-by-step:
1. Identify the Baking Times:
- Scones take 15 minutes to bake.
- Muffins take 12 minutes to bake.
- Cookies take 10 minutes to bake.
2. Understand the Problem:
- We need to find a moment in time that is a multiple of each of these individual times (15, 12, and 10 minutes). This means we want the smallest number that all three of these numbers divide into without leaving a remainder.
3. Find the Least Common Multiple (LCM):
- The LCM of a set of numbers is the smallest positive integer that is divisible by all of the numbers in the set.
4. Calculate the LCM:
- Consider the prime factorizations:
- 15 = 3 × 5
- 12 = 2² × 3
- 10 = 2 × 5
- For the LCM, take the highest power of each prime number that appears in any factorization:
- Take 2² (from 12)
- Take 3 (from both 15 and 12)
- Take 5 (from both 15 and 10)
- Multiply these together: [tex]\(2² \times 3 \times 5 = 4 \times 3 \times 5 = 60\)[/tex].
5. Conclusion:
- The least common multiple of 15, 12, and 10 is 60. So, after 60 minutes, Caylan will first be able to remove the scones, muffins, and cookies from the oven at the same time.
Therefore, the answer is that Caylan will first remove all the trays at the same time after 60 minutes.
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