To find the Least Common Multiple (LCM) of 25, 30, 35, and 40, we will first find the prime factorizations of each number:

- \( 25 = 5^2 \)
- \( 30 = 2 \times 3 \times 5 \)
- \( 35 = 5 \times 7 \)
- \( 40 = 2^3 \times 5 \)

Now, the LCM is determined by taking the highest powers of all the prime factors present in any of the numbers:

- For the factor 2, the highest power is \( 2^3 \) (from 40).
- For the factor 3, the highest power is \( 3^1 \) (from 30).
- For the factor 5, the highest power is \( 5^2 \) (from 25).
- For the factor 7, the highest power is \( 7^1 \) (from 35).

The LCM is the product of these highest powers:
\[
LCM = 2^3 \times 3^1 \times 5^2 \times 7^1 = 8 \times 3 \times 25 \times 7 = 4200
\]

Therefore, the LCM of 25, 30, 35, and 40 is **4200**.

Would you like more details or have any questions?

Here are five related questions:
1. How does the LCM differ from the GCD (Greatest Common Divisor)?
2. What is the LCM of 12, 18, and 24?
3. How can you use the LCM to solve problems involving adding or subtracting fractions?
4. What are some real-life applications of finding the LCM?
5. How would you find the LCM if the numbers were much larger?

**Tip:** The LCM is especially useful when adding or subtracting fractions with different denominators.

Learn how to find the Least Common Multiple (LCM) of 25, 30, 35, and 40 by using prime factorization. This step-by-step guide covers the LCM formula and explains the prime factorization process. Suitable for students in Grades 6-8.

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