Question

What is the sum of digits of the least number which when divided by 15, 16, 18 and 25 leaves the same remainder 6 in each case and is divisible by 11?
1. 16
2. 15
3. 17
4. 18

Answer 1

Correct Answer - Option 2 : 15

Given:

When the number is divided by 15, 16, 18 and 25 then leave the same remainder 6

Concept:

LCM of the numbers = Product of the greatest power of each prime factor involved in the number

Calculation:

⇒ The least number which is completely divisible by 15, 16, 18, and 25

LCM of (15, 16, 18, 25) = 2⁴ × 3² × 5² = 16 × 9 × 25 = 3600

⇒ Number gives same remainder 6 then number = 3600K + 6     ----(Where K is a natural number)

⇒ When K = 1 then number be

⇒ (3600 × 1) + 6 = 3606     ----(Which is not divisible by 11)

⇒ For K = 1, 2, 3, 4, 5, 6, 7, 8     ----(Not divisible by 11)

⇒ For K = 9

⇒ (3600 × 9) + 6 = 32406     ----(Which is divisible by 11)

⇒ Sum of the digits of the 32406 = 3 + 2 + 4 + 0 + 6 = 15

∴ The required result will be 15.