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The image shows a word problem regarding the circumferences of wheels. From what I can decipher, here is the text of the problem:

"The circumferences of three toy wheels are 12 cm, 14 cm, and 15 cm, respectively. If the three wheels start rolling together, find the minimum number of revolutions they each will make before all the wheels make complete revolutions."

This question is asking you to find the least common multiple (LCM) of the circumferences of the wheels to determine the number of revolutions they will each make before completing a full cycle together.

Let's solve this problem:

1. **Circumferences of the wheels**: 12 cm, 14 cm, and 15 cm.
2. **Find the LCM**: The smallest number that is a multiple of all three circumferences.

To calculate the LCM:
- Prime factorization of 12: \( 2^2 \times 3 \)
- Prime factorization of 14: \( 2 \times 7 \)
- Prime factorization of 15: \( 3 \times 5 \)

LCM = \( 2^2 \times 3 \times 5 \times 7 = 420 \)

Therefore, the least common multiple (LCM) of 12, 14, and 15 is 420 cm. 

Now, to find the number of revolutions each wheel makes:
- For the 12 cm wheel: \( 420 / 12 = 35 \) revolutions.
- For the 14 cm wheel: \( 420 / 14 = 30 \) revolutions.
- For the 15 cm wheel: \( 420 / 15 = 28 \) revolutions.

Thus, each wheel will make 35, 30, and 28 revolutions respectively before all wheels make a complete revolution at the same time.

Would you like further details or have any questions?

Here are 5 questions that expand on this concept:
1. What is the LCM and how is it useful in solving problems involving cycles?
2. How can the prime factorization method simplify finding the LCM of large numbers?
3. What is the relationship between LCM and GCD (Greatest Common Divisor)?
4. Can LCM be used to find synchronized events in real-world situations? Give examples.
5. How does the concept of periodicity relate to LCM in mathematics?

**Tip:** Always use prime factorization to find the LCM when working with multiple numbers, as it ensures accuracy and efficiency.

The circumferences of three toy wheels are 12 cm, 14 cm, and 15 cm, respectively. If the three wheels start rolling together, find the minimum number of revolutions they each will make before all the wheels make complete revolutions.

Learn how to find the least common multiple (LCM) of the circumferences of three toy wheels (12 cm, 14 cm, and 15 cm). This problem involves key math concepts such as prime factorization and LCM calculation, making it perfect for students in Grades 6-8.

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