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?

18

LCM of 15, 18 and 36 → 180

∴ Least number = 180K + 9 {which is exactly divisible by 11 for certain value of}

when K = 6,

Number  = 180 × 6 + 9 = 1089 which is exactly divisible by 11

Sum of digits of number = 1 + 0 + 8 + 9 = 18