Multiple choice

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?

  1. 1080

  2. 1089

  3. 1071

  4. 1279

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

If N leaves remainder 9 when divided by 15, 18, 36, then N - 9 is divisible by LCM(15, 18, 36) = 180. So N = 180k + 9. For divisibility by 11: 180k + 9 ≡ 4k + 9 ≡ 0 (mod 11), so 4k ≡ 2 (mod 11), giving k = 6. N = 180(6) + 9 = 1089.