Question

what is the least number that must be added to 2000 so that the sum is divisible exactly by 10, 12, 16 and 18?

Answer 1

100 should be added to it

Answer 2

Answer:

The required number  that must be added to 2000 so that the sum is divisible exactly by 10, 12, 16 and 18 is 160.

Step-by-step explanation:

To find : The least number that must be added to 2000 so that the sum is divisible exactly by 10, 12, 16 and 18?

Solution :  

We find the LCM of 10, 12, 16 and 18.

2 | 10  12  16  18

2 | 5   6    8    9

2 | 5   3    4    9

2 | 5   3    2    9  

3 | 5   3    1     9

3 | 5   1    1      3

5 | 5   1    1      1

  | 1   1    1      1

$LCM(10,12,16,18)=2\times 2\times 2\times 2\times 3\times 3\times 5$

$LCM(10,12,16,18)=720$

Now, Divide 2000 by 720

$\frac{2000}{720}=2.77$

The least number is 3.

So, $720\times 3=2160$

The least number that must be added to 2000 so that the sum is divisible exactly by 10, 12, 16 and 18 is given by,

$2160-2000=160$

Therefore, The required number  that must be added to 2000 so that the sum is divisible exactly by 10, 12, 16 and 18 is 160.