What is the smallest number divisible by all numbers 1 to 10?

The smallest number divisible by all numbers from 1 to 10 is 2520.

This number is also known as the Least Common Multiple (LCM) of the numbers 1 through 10. To find it, we need to consider the prime factorization of each number:

• 1 = 1
• 2 = 2
• 3 = 3
• 4 = 2 x 2 = 2²
• 5 = 5
• 6 = 2 x 3
• 7 = 7
• 8 = 2 x 2 x 2 = 2³
• 9 = 3 x 3 = 3²
• 10 = 2 x 5

To find the LCM, we take the highest power of each prime number that appears in any of the factorizations:

• 2³ = 8
• 3² = 9
• 5 = 5
• 7 = 7

Then, we multiply these together:

8 x 9 x 5 x 7 = 2520

Therefore, 2520 is the smallest number that is perfectly divisible by all numbers from 1 to 10.