To find the least common multiple (LCM) of 25, 45, and 75, we follow these steps:

### Step 1: Prime Factorization
- \( 25 = 5^2 \)
- \( 45 = 3^2 \times 5 \)
- \( 75 = 3 \times 5^2 \)

### Step 2: Take the highest powers of all primes involved
- The prime factors are 3 and 5.
- For 3, the highest power is \( 3^2 \) (from 45).
- For 5, the highest power is \( 5^2 \) (from 25 and 75).

### Step 3: Multiply the highest powers together
\[
\text{LCM} = 3^2 \times 5^2 = 9 \times 25 = 225
\]

So, the least common multiple (LCM) of 25, 45, and 75 is **225**.

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Here are 5 related questions for further exploration:
1. What is the LCM of 12, 15, and 20?
2. How is the greatest common divisor (GCD) of numbers related to their LCM?
3. Can you find the LCM of 30, 40, and 50?
4. How do you compute the LCM of two numbers using their prime factorizations?
5. What is the relation between LCM and the product of numbers?

**Tip:** The LCM is always at least as large as the largest number in the set.

Discover how to calculate the least common multiple (LCM) of 25, 45, and 75 by using the prime factorization method. This step-by-step solution highlights the use of prime factor powers and explains the key concepts of number theory, perfect for Grades 6-8 students.

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