Correct option is B
Given:
We are asked to find which number is divisible by all the natural numbers from 1 to 10 (both inclusive).
Concept Used:
To check divisibility by all numbers from 1 to 10, we need to find the Least Common Multiple (LCM) of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10.
A number divisible by all the numbers from 1 to 10 must be divisible by the LCM of these numbers.
Solution:
The prime factorizations of the numbers are:
1 = 1
2 = 2
3 = 3
4 = 2^2
5 = 5
6 = 2 × 3
7 = 7
8 = 2^3
9 = 3^2
10 = 2 × 5
LCM of 1 to 10 = 2^3 × 3^2 × 5 × 7 = 2520
Now, we check each option for divisibility by 2520:
A. 1000 is not divisible by 7, so it is not divisible by all numbers from 1 to 10.
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