To find the Least Common Multiple (LCM) of 385, 700, and 1295, we first need to find the prime factorizations of these numbers.

### Step 1: Prime factorization of each number.

- **385**:  
  \( 385 = 5 \times 7 \times 11 \)

- **700**:  
  \( 700 = 2^2 \times 5^2 \times 7 \)

- **1295**:  
  \( 1295 = 5 \times 7 \times 37 \)

### Step 2: LCM Calculation

To find the LCM, take the highest power of each prime factor that appears in any of the numbers.

- \( 2^2 \) (from 700)
- \( 5^2 \) (from 700)
- \( 7^1 \) (common in all three numbers)
- \( 11^1 \) (from 385)
- \( 37^1 \) (from 1295)

### Step 3: Multiply these together
\[
LCM = 2^2 \times 5^2 \times 7 \times 11 \times 37
\]

\[
LCM = 4 \times 25 \times 7 \times 11 \times 37
\]
Let's calculate this step by step:

\[
4 \times 25 = 100
\]
\[
100 \times 7 = 700
\]
\[
700 \times 11 = 7700
\]
\[
7700 \times 37 = 284,900
\]

### Final Answer:
The LCM of 385, 700, and 1295 is **284,900**.

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Do you want further details or have any questions?

Here are 5 related questions:
1. What is the LCM of 12, 15, and 20?
2. How does the LCM differ from the GCD (Greatest Common Divisor)?
3. Can you find the LCM of two prime numbers?
4. What role do prime factorizations play in finding the LCM?
5. How is the LCM used in solving problems involving fractions?

**Tip:** Always break down numbers into their prime factors when finding the LCM for better accuracy.

Discover how to calculate the Least Common Multiple (LCM) of 385, 700, and 1295 using prime factorization. This step-by-step solution covers key number theory concepts, including prime factors and LCM calculation. Suitable for students in Grades 7-9.

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