Question

The least number that should be added to 57 so that the sum is exactly divisible by 2, 3, 4 and 5 is

Answer 1

Firstly, we find the LCM of 2,3,4 and 5

2 | 2, 3, 4, 5

2 | 1, 3, 2, 5

3 | 1, 3, 1, 5

5 | 1, 1, 1, 5

| 1 , 1 , 1 , 1

LCM( 2, 3,4,5) = 2× 2× 3× 5 = 60

Subtract 57 from 60 , we get

= 60 -57 = 3

So, 3 is the least number that should be added to 57 .

Answer 2

Given:

Number 57

Sum exactly divisible by 2, 3, 4, 5.

To find:

The least number to be added to 57.

Solution:

We need to find a number that should be added to $57$. Let this number be $x$.

On adding $x$ with $57$ we get a sum of $y$. This $y$ should be divisible by $2,3,4,5$. If $y$ has to be divisible by $2,3,4,5$, then it should have prime factors as $2,3,4,5$.  

On calculating the LCM of $2,3,4,5$ we we can determine $y$.

$LCM(2,3,4,5)=60$

Subtract $57$ from $60$ to determine the least number $x$.

$60-57=3$

Hence, $3$ is the least number that should be added to $57$ so that the sum, $60$, is exactly divisible by $2,3,4,5$ .

$3$ is the least number that should be added to $57$ so that the sum, $60$, is exactly divisible by $2,3,4,5$ .