If the product of three consecutive positive integers is 15600

• Numbers

If the product of three consecutive positive integers is 15600 then the sum of the squares of these integers is

1. 1777
2. 1785
3. 1875
4. 1877

Answer

Given, (n – 1) × (n) × (n + 1) = 15600

As 15600 has 2 zeroes in it, one of n – 1, n or n + 1 should be a multiple of 25.

Dividing 15600 by 25, we get 624, but 624 = 24×26 so, the numbers are 24, 25 and 26

24² + 25² + 26² = 1877 

The correct option is D.