Question : What is the least number which when divided by 15, 18 and 36 leaves the same remainder 9 in each case and is divisible by 11?
Option 1: 1269
Option 2: 1071
Option 3: 1089
Option 4: 1080
Correct Answer: 1089
Solution :
15 = 3 × 5
18 = 2 × 3 × 3
36 = 2 × 2 × 3 × 3
LCM of 15, 18, 36 = 2 × 2 × 3 × 3 × 5 = 180
Required number = $180x + 9$
So, $180x + 9$ is a multiple of 11.
⇒ $176x + 4x + 9$ is a multiple of 11
⇒ $4x+9$ is a multiple of 11
⇒ $4×6+9 = 33$ is a multiple of 11
⇒ $x = 6$
$\therefore$ The required number = 180 × 6 + 9 = 1089
Hence, the correct answer is 1089.
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