Question

Which of the following represents the largest 3 digit number which can be added to 425 in order to make
the derived number divisible by each of 6, 12, 16, 27..........?
A) 921
B) 998
C) 871
D) 827​

Answer 1

The correct option is (C) 871.

We have to find the largest 3 digit number which can be added to 425 in order to make the derived number divisible by each 6, 12, 16 and 27.

First find LCM of 6, 12 , 16 , 27

• prime factors of 6 = 2 × 3
• prime factors of 12 = 2² × 3
• prime factors of 16 = 2⁴
• prime factors of 27 = 3³

∴ LCM of {6, 12, 16, 27} = 2⁴ × 3³ = 432

Here, 425 + ( a three digit largest number) = 432 × n

where n is integer.

If we take n = 3 , 432 × 3 = 1296

∴ 425 + a three digit largest number = 1296

⇒a three digit largest number = 1296 - 425 = 871

Therefore the three digit largest number is 871 which can be added to 425 in order to make the derived number divisible by 6, 12 , 16 and 27.