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Find the least multiple of 13 which when divided by 6, 8 and 12 leaves 5, 7 and 11 as remainders respectively? A. 143 B. 169 C. 260 D. 221

Correct answer: A. 143

  • A. 143
  • B. 169
  • C. 260
  • D. 221

Explanation

Each remainder is one less than its divisor, so the number plus 1 must be divisible by 6, 8 and 12. Their least common multiple is 24, giving n = 24k - 1; among the options, 143 = 24 x 6 - 1 and 143 ÷ 13 = 11, so it satisfies every condition. The likely mistake is option b, which is divisible by 13 but does not give all the required remainders.

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