To find the least common multiple (LCM) and greatest common divisor (GCD) of 6 and 10, we can use the following methods:

### 1. **Finding the LCM (Least Common Multiple)**:
   The LCM of two numbers is the smallest positive number that is divisible by both. 

   - Prime factorization of 6: \( 6 = 2 \times 3 \)
   - Prime factorization of 10: \( 10 = 2 \times 5 \)

   Now, take the highest powers of all primes appearing in the factorization:
   - For 2: the highest power is \( 2^1 \)
   - For 3: the highest power is \( 3^1 \)
   - For 5: the highest power is \( 5^1 \)

   Multiply these together:  
   \( 2^1 \times 3^1 \times 5^1 = 30 \)

   So, the **LCM of 6 and 10 is 30**.

### 2. **Finding the GCD (Greatest Common Divisor)**:
   The GCD of two numbers is the largest number that divides both.

   - Prime factorization of 6: \( 6 = 2 \times 3 \)
   - Prime factorization of 10: \( 10 = 2 \times 5 \)

   The common prime factor is \( 2^1 \).

   So, the **GCD of 6 and 10 is 2**.

### Summary:
- **LCM(6, 10) = 30**
- **GCD(6, 10) = 2**

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the LCM of 12 and 15?
2. How do you find the GCD of 24 and 36 using the prime factorization method?
3. Can you explain how to use the Euclidean algorithm to find the GCD?
4. What is the relationship between LCM and GCD for any two numbers?
5. How can you find the LCM and GCD of more than two numbers?

**Tip**: The product of the GCD and LCM of two numbers is equal to the product of the numbers themselves!

Learn how to calculate the least common multiple (LCM) and greatest common divisor (GCD) of 6 and 10 using prime factorization. This tutorial covers key number theory concepts, including prime factorization, LCM, and GCD. Suitable for Grades 5-7.

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