What is the Least Common Multiple of 160 and 180?

To find the Least Common Multiple (LCM) of 160 and 180, we follow these steps:

### Step 1: Prime Factorization of Both Numbers
1. **160**:  
   - \( 160 = 2^5 \times 5 \)
2. **180**:  
   - \( 180 = 2^2 \times 3^2 \times 5 \)

### Step 2: Take the Highest Powers of Each Prime Factor
- For 2: The highest power is \( 2^5 \) (from 160).
- For 3: The highest power is \( 3^2 \) (from 180).
- For 5: The highest power is \( 5^1 \) (common to both).

### Step 3: Multiply the Highest Powers Together
\[
\text{LCM} = 2^5 \times 3^2 \times 5 = 32 \times 9 \times 5 = 1440
\]

### Final Answer:
The Least Common Multiple of 160 and 180 is **1440**.

Would you like further details or have any questions?

Here are some related questions you might find helpful:
1. What is the greatest common divisor (GCD) of 160 and 180?
2. How do you find the LCM using the GCD method?
3. What are the applications of LCM in real-world problems?
4. How does LCM differ from the least common denominator (LCD)?
5. Can LCM be used to solve problems involving fractions?

**Tip**: Knowing prime factorization simplifies finding both LCM and GCD of numbers.

Discover how to find the Least Common Multiple (LCM) of 160 and 180 using prime factorization. This detailed explanation includes key concepts like number theory and the LCM formula. Perfect for students in Grades 6-8.

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