What is the least common multiple of 6 and 10

The least common multiple (LCM) of two numbers is the smallest positive integer that is divisible by both numbers.

To find the LCM of 6 and 10:

1. **Prime factorization**:
   - \( 6 = 2 \times 3 \)
   - \( 10 = 2 \times 5 \)

2. **Take the highest powers of all prime factors**:
   - \( 2^1 \) (from both 6 and 10)
   - \( 3^1 \) (from 6)
   - \( 5^1 \) (from 10)

3. **Multiply the highest powers together**:
   - \( 2^1 \times 3^1 \times 5^1 = 30 \)

Thus, the least common multiple of 6 and 10 is **30**.

Would you like more details or have any questions?

Here are some related questions:
1. What is the greatest common divisor (GCD) of 6 and 10?
2. How do you find the LCM of more than two numbers?
3. How is the LCM related to the GCD?
4. Can you find the LCM using the formula involving GCD?
5. What is the LCM of 6, 10, and 15?

**Tip**: The LCM of two numbers is always equal to the product of the numbers divided by their greatest common divisor.

What is the least common multiple of 6 and 10?

Discover how to calculate the least common multiple (LCM) of 6 and 10 using prime factorization. This solution covers the prime factorization method and key mathematical concepts like LCM and GCD. Suitable for middle school students (Grades 6-8).

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