What is the least number that is divisible by all natural numbers from 1 to 10 (including 1 and 10)?
Question
What is the least number that is divisible by all natural numbers from 1 to 10 (including 1 and 10)?
Solution
The least number that is divisible by all natural numbers from 1 to 10 is called the least common multiple (LCM) of the numbers from 1 to 10. Here are the steps to find it:
- List the prime numbers less than 10: 2, 3, 5, 7.
- For each prime number, find the highest power of that prime which is less than or equal to 10. This is 2^3 (or 8), 3^2 (or 9), 5^1 (or 5), and 7^1 (or 7).
- Multiply these numbers together: 8 * 9 * 5 * 7 = 2520.
So, the least number that is divisible by all natural numbers from 1 to 10 is 2520.
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