Question

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

Answer 1

To find Least number that is divisible by all the numbers between $1$ and $10$ (both inclusive) Let us first find the L.C.M of all the numbers between 1 and 10 (both inclusive)

$1=1$

$2=2$

$3=3$

$4=2^2$

$5=5$

$6=2\times 3$

$7=7$

$8=2^3$

$9=3^2$

$10=2\times 5$

L.C.M $=$ Product of the highest power of the prime factors including other factors

$=2^3\times 3^2\times 5\times 7$

$=8\times 9\times 5\times 7$

$=2520$

Hence $2520$ is the least number that is divisible by all the numbers between $1$ and $10$ (both inclusive)