Produce the least positive number that is divisible by 2, 3, 4, 5, 6, 7, 8, 9, 10, 11.

The number is___

To find the least positive number divisible by all the numbers from 2 to 11, we need to calculate the least common multiple (LCM) of these numbers.

### Step-by-Step Calculation:

1. **Prime factorizations** of each number:
   - 2 = \( 2 \)
   - 3 = \( 3 \)
   - 4 = \( 2^2 \)
   - 5 = \( 5 \)
   - 6 = \( 2 \times 3 \)
   - 7 = \( 7 \)
   - 8 = \( 2^3 \)
   - 9 = \( 3^2 \)
   - 10 = \( 2 \times 5 \)
   - 11 = \( 11 \)

2. **Take the highest powers** of each prime factor:
   - For 2: The highest power is \( 2^3 \) (from 8).
   - For 3: The highest power is \( 3^2 \) (from 9).
   - For 5: The highest power is \( 5 \) (from 5 or 10).
   - For 7: The highest power is \( 7 \) (from 7).
   - For 11: The highest power is \( 11 \) (from 11).

3. **Multiply these highest powers together** to get the LCM:
   \[
   \text{LCM} = 2^3 \times 3^2 \times 5 \times 7 \times 11
   \]
   \[
   \text{LCM} = 8 \times 9 \times 5 \times 7 \times 11 = 27720
   \]

Thus, the least positive number divisible by 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11 is **27720**.

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Would you like more details or have any questions? 

Here are 5 related questions:
1. What is the least common multiple of 2, 3, and 5?
2. How would the answer change if the range extended to 12?
3. What is the greatest common divisor (GCD) of 8 and 9?
4. How does prime factorization help in finding LCM?
5. What is the difference between GCD and LCM?

**Tip:** When finding the LCM, always use the highest powers of prime factors from the given numbers.

Produce the least positive number that is divisible by 2, 3, 4, 5, 6, 7, 8, 9, 10, 11. The number is___

Learn how to find the least positive number divisible by the numbers 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11. This problem uses key concepts from number theory, including prime factorization and the least common multiple (LCM), to arrive at the solution. Suitable for students in Grades 6-8.

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