What is the sum of the digits of the least number which when divided by 15, 18, and 36 leaves the same remainder 9 in each case and is divisible by 11?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e 18.
The least number which will be completely divisible by 15, 18, and 36 will be the LCM of 15, 18, and 36.
⇒ LCM of 15, 18 and 36 = 180
The least number will be completely divisible by the 15, 18, and 36 and leaves the remainder 9 = 180k + 9
Where,
k = natural number
when k = 1
⇒ 189
Here 189 is not divisible by 11.
When k = 1, 2, 3, 4, 5. The number is not divisible by 11.
Now, k = 6
Number = 180 × 6 + 9
⇒ Number = 1089
The number 1089 is divisible by 11.
Sum of digits = 1 + 0 + 8 + 9 = 18
Thus,
The sum of the digits of the least number which when divided by 15, 18 and 36 leaves the same remainder 9 in each case and is divisible by 11 is 18.