Question

find the least number which is divisible by all numbers from 1 to 10 (both inclusive).

Answer 1

WE WILL TAKE LCM FROM 1 TO 10 =2520
THE LEAST NUMBER IS 2520

Answer 2

We want LCM(1,2,3,4,5,6,7,8,9,10)
We can ignore 1, since any counting number is divisible by 1.
We prime factor each of the counting numbers from 2 to 10 
2 = 2
3 = 3
4 = 2*2
5 = 5
6 = 2*3
7 = 7
8 = 2*2*2
9 = 3*3

10 = 2*5 
The LCM of all those must have as many factors of
each prime that appears in any factorization 
2 appears at most 3 times as a factor of 8
3 appears at most 2 times as a factor of 9
5 appears at most 1 time as a factor if 5 and 10
7 appears at most 1 time as a factor of 7

So the LCM has 
3 factors of 2, 2 factors of 3, and 1 facor each of 5 and 7 
LCM = 2*2*2*3*3*5*7 = 2520