Question

The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is?

${\text{A}}{\text{.}}$ $10$

${\text{B}}{\text{.}}$ $100$

${\text{C}}{\text{.}}$ $504$

${\text{D}}{\text{.}}$ $2520$

Answer 1

Hint: To find out the least number divisible by all the numbers from 1 to 10 which we need to find out the Least Common Multiple of all the numbers from 1 to 10.

Complete step-by-step answer:

According to the question, we have to find out the least numbers divisible by all the numbers from 1 to 10, so here we can use the below method.

We need to calculate the L.C.M of the following number that is,

$1 = 1$

$2 = 2 \times 1$

$3 = 3 \times 1$

$4 = 2 \times 2$

$5 = 5 \times 1$

$6 = 2 \times 3$

$7 = 7 \times 1$

$8 = 2 \times 2 \times 2$

$9 = 3 \times 3$

$10 = 2 \times 5$

Now we have the lowest common multiple of these number will be

$ \Rightarrow $$1 \times 2 \times 2 \times 2 \times 3 \times 3 \times 5 \times 7$

$ \Rightarrow 2520$

Hence, the least number divisible by all the numbers from 1 to 10$ = 2520$

Note: Approach this question with the concept of L.C.M. In arithmetic and number theory, the least common multiple, lowest common multiple, or smallest common multiple of two integers a and b, usually denoted by LCM (a, b), is the smallest positive integer that is divisible by both a and b.