Question

Find the least number which is added with 7000 to get the sum divisible by 12, 16, 18, 24.​

Answer 1

Answer:

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

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 5LCM(10,12,16,18)=2×2×2×2×3×3×5

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

Now, Divide 2000 by 720

\frac{2000}{720}=2.77

720

2000

=2.77

The least number is 3.

So, 720\times 3=2160720×3=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=1602160−2000=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.