Find the least number that is divisible by all the numbers between $1$ and $10$ (both inclusive).

The least number that is divisible by

$(1,2,3,4,5,6,7,8,9,10)$

we have to take $LCM$ of given numbers.

As all number are divisible by $1$, than

we neglect if

using prime factors

$2=2,3=3,4=2\times 2,5=5$

$6=2\times 3,7=7,8=2\times 2\times 2,9=3\times 3,10=2\times 5$

Now $LCM$ of given number is $=2\times 2\times 2\times 3\times 3\times 5\times 7\times$

$=8\times 9\times 35$

$LCM=2520$

$\therefore 2520$ is least number divisible by $\left(\mathrm{1.....10}\right)$ both inclusive.