The smallest number divisible by all numbers from 2 to 9 is 2520.
Understanding the Least Common Multiple (LCM)
To find the smallest number divisible by a set of numbers, we need to determine their Least Common Multiple (LCM). The LCM is the smallest positive integer that is divisible by each of the numbers in the set without leaving a remainder.
Finding the LCM of 2 to 9
The provided reference states: "To find the lowest common multiple of the numbers, let's find the factors of the given numbers for which we have to find the LCM of each number. Hence, \[2520\] is the number which is completely divided by any number between 2 to 9."
This means that when you divide 2520 by any number from 2 to 9, the result will always be a whole number. Let's verify this:
- 2520 / 2 = 1260
- 2520 / 3 = 840
- 2520 / 4 = 630
- 2520 / 5 = 504
- 2520 / 6 = 420
- 2520 / 7 = 360
- 2520 / 8 = 315
- 2520 / 9 = 280
As you can see, each division results in a whole number, confirming that 2520 is the smallest number divisible by all integers from 2 to 9.
Key Takeaway
- The smallest number divisible by a set of numbers is their LCM.
- The LCM of the numbers from 2 to 9 is 2520.
