find the LCM using the listing and continous division method of 10,15,25

Let's find the **Least Common Multiple (LCM)** of 10, 15, and 25 using both the **listing multiples method** and the **continuous division method**.

### 1. Listing Multiples Method:

For each number, we list the first few multiples and find the smallest common one.

- **Multiples of 10**:  
  10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, ...

- **Multiples of 15**:  
  15, 30, 45, 60, 75, 90, 105, 120, 135, 150, ...

- **Multiples of 25**:  
  25, 50, 75, 100, 125, 150, ...

The smallest common multiple in all three lists is **150**.

So, the **LCM of 10, 15, and 25** is **150**.

### 2. Continuous Division Method:

We repeatedly divide by the smallest prime factors common to all three numbers until we can't divide any further.

#### Step-by-Step:
We divide 10, 15, and 25 using common prime factors.

| Step | Divisor | 10  | 15  | 25  |
|------|---------|-----|-----|-----|
| 1    | 2       | 5   | 15  | 25  |
| 2    | 3       | 5   | 5   | 25  |
| 3    | 5       | 1   | 1   | 5   |
| 4    | 5       | 1   | 1   | 1   |

Now that all numbers are 1, the process stops.

- The LCM is obtained by multiplying all the divisors together:  
  \( 2 \times 3 \times 5 \times 5 = 150 \)

Thus, the **LCM of 10, 15, and 25** is **150** using both methods.

---

Do you have any questions or would you like more details on these methods?

Here are 5 related questions to consider:
1. What is the LCM of 12, 18, and 24 using the listing method?
2. How is the LCM different from the greatest common divisor (GCD)?
3. Can you find the LCM of 14, 21, and 35 using the continuous division method?
4. What happens if two numbers are relatively prime? How does it affect their LCM?
5. Why is it important to find the LCM in solving word problems?

**Tip**: When using the continuous division method, always divide by the smallest prime number possible at each step.

find the LCM using the listing and continuous division method of 10,15,25

Discover how to find the Least Common Multiple (LCM) of 10, 15, and 25 using both the listing multiples method and the continuous division method. This step-by-step guide is ideal for students in Grades 5-7, covering key concepts in number theory and arithmetic.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation