The least number which should be added to 4707 so that the sum is exactly divisible by 4, 5, 6 and 8 is:

Correct option is D

Given:

The number 4707. We need to find the least number to add to it so that the sum is exactly divisible by 4, 5, 6, and 8.

Concept Used:

Least Common Multiple (LCM): The smallest number that is exactly divisible by each of the numbers 4, 5, 6, and 8.

Solution:

Find the LCM of 4, 5, 6, and 8:

Prime factorization:

4 = $$2^2$$​​

5 = 5

6 = 2 $$\times$$​ 3

8 =$$2^3$$​​

LCM = 2³$$\times$$ 3 $$\times$$ 5 = 8$$\times$$3$$\times$$5 = 120​​​​

Divide 4707 by the LCM (120) and find the remainder:

4707 ÷ 120 = 39 with a remainder of 27.

Calculate the number to be added:

Since the remainder is 27, it means 4707 is 27 more than a multiple of 120.

To find the next multiple of 120, we subtract the remainder from 120:

120 - 27 = 93

Therefore, the least number that should be added to 4707 is 93.

Option (d) is right.