Find the Least Number Divisible by All Numbers from 1 to 10
Video Explanation
Watch the video below to understand the complete solution step by step:
Solution
Question: Find the least number that is divisible by all the numbers between 1 and 10 (both inclusive).
Step 1: Identify the Mathematical Concept
The least number divisible by all the given numbers is their LCM (Least Common Multiple).
Step 2: Prime Factorization of Numbers from 1 to 10
1 = 1
2 = 2
3 = 3
4 = 22
5 = 5
6 = 2 × 3
7 = 7
8 = 23
9 = 32
10 = 2 × 5
Step 3: Find the LCM
Take the highest powers of all prime factors:
LCM = 23 × 32 × 5 × 7
LCM = 8 × 9 × 5 × 7
LCM = 2520
Final Answer
∴ The least number that is divisible by all the numbers from 1 to 10 is 2520.
Conclusion
Thus, by finding the LCM of all numbers from 1 to 10, we conclude that the required least number is 2520.