Find the Least Number that is Divisible by all the Numbers from 1 to 10 (Both Inclusive)

By Mandeep Kumar|Updated : May 18th, 2023

To find: the number that is divisible by all of the integers from 1 to 10, as well as the smallest number among these numbers.

The LCM of these numbers is the smallest number that is divisible by all of the numbers from 1 to 10 i.e. 1,2,3,4,5,6,7,8,9,10.

First we have to find the factors of 1,2,3,4,5,6,7,8,9,10 which are as follows:

1 = 1

2 = 1 × 2

3 = 1 × 3

4 = 1 × 2 × 2

5 = 1 × 5

6 = 1 × 2 × 3

7 = 1 × 7

8 = 1 × 2 × 2 × 2

9 = 1 × 3 × 3

10 = 1 × 2 × 5

So, the LCM of 1,2,3,4,5,6,7,8,9,10 = 1×2×2×2×3×3×5×7 = 2520.

Therefore, the least number that is divisible by all the numbers from 1 to 10 (Both Inclusive) is 2520.

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Least Number that is Divisible by all the Numbers from 1 to 10

As discussed above, 2520 is the smallest number that is divisible by all the numbers between 1 and 10. To determine that candidates should have an idea of how to find LCM that is Least Common Factor.

The Least Common Multiple (LCM) is also known as the Least Common Divisor and the Lowest Common Multiple. LCM(a,b) is the smallest positive integer that is evenly divisible by both a and b for two integers a and b.

Example: LCM (2,3,4)

Multiple of 2: 2,4,6,8,10,12,14, and so on.

Multiple of 3: 3,6,9,12,15,18, and so on.

Multiple of 4: 4, 8, 12, 16, 20, and so on

The smallest number that is in bold in the multiples of 2, 3, and 4 is the LCM of 2, 3, and 4.

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