The Field hockey team, and the soccer team share a field at there last practice. If the Field hockey team uses the field every four days and the Soccer team uses the field every six days, how many days after their last practice will they share the field again?

To determine when the Field Hockey team and the Soccer team will share the field again, we need to find the **Least Common Multiple (LCM)** of 4 days (Field Hockey team's schedule) and 6 days (Soccer team's schedule). 

The steps are as follows:

1. **Prime factorization of the numbers:**
   - 4 = \( 2^2 \)
   - 6 = \( 2^1 \times 3^1 \)

2. **Identify the highest powers of all prime factors:**
   - For 2: the highest power is \( 2^2 \) (from 4)
   - For 3: the highest power is \( 3^1 \) (from 6)

3. **Multiply these highest powers:**
   \[
   2^2 \times 3^1 = 4 \times 3 = 12
   \]

Thus, the **LCM of 4 and 6 is 12**. Therefore, the Field Hockey and Soccer teams will share the field again in **12 days**.

Would you like further details or have any questions about the steps? Here are some related questions to consider:

1. What is the LCM of 8 and 12?
2. How do you find the greatest common divisor (GCD)?
3. Can you find the next time the teams share the field if one team uses it every 5 days and the other every 7 days?
4. Why is the LCM important when working with recurring events?
5. How does prime factorization help in finding the LCM?

**Tip:** When finding the LCM, always consider the highest powers of all prime factors involved.

The Field hockey team and the soccer team share a field at their last practice. If the Field hockey team uses the field every four days and the soccer team uses the field every six days, how many days after their last practice will they share the field again?

Discover how to find out when the Field hockey and soccer teams will share the field again by calculating the Least Common Multiple (LCM) of 4 and 6 days. This solution involves number theory and prime factorization, suitable for students in Grades 5-7.

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