What is the least common multiple of 3, 6, and 10?

To find the least common multiple (LCM) of 3, 6, and 10, follow these steps:

1. **Prime Factorization**:
   - 3 is already a prime number: \(3 = 3^1\)
   - 6 can be factored as \(6 = 2^1 \times 3^1\)
   - 10 can be factored as \(10 = 2^1 \times 5^1\)

2. **Identify the highest powers of each prime factor**:
   - The highest power of 2 is \(2^1\) (from 6 and 10).
   - The highest power of 3 is \(3^1\) (from 3 and 6).
   - The highest power of 5 is \(5^1\) (from 10).

3. **Multiply these together**:
   \[
   \text{LCM} = 2^1 \times 3^1 \times 5^1 = 2 \times 3 \times 5 = 30
   \]

Thus, the least common multiple of 3, 6, and 10 is **30**.

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you find the greatest common divisor (GCD) of 3, 6, and 10?
2. What is the LCM of 4, 5, and 12?
3. How do you find the LCM using the GCD method?
4. What is the relation between GCD and LCM?
5. Can you find the LCM of decimal numbers?

**Tip:** The LCM of two or more numbers is always greater than or equal to the largest of the numbers.

Discover how to find the least common multiple (LCM) of 3, 6, and 10 through prime factorization. This step-by-step guide helps students in Grades 6-8 understand the key concepts behind LCM calculation using prime numbers. The solution covers important factors and theorems for calculating LCM.

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