Multiple choice

Find the greatest number of six digits which when divided by 15, 20, 24 and 60 leaves remainder 12, 17, 21 and 57 respectively. छः अंको की बड़ी से बड़ी संख्या ज्ञात कीजिये जिसे जब 15, 20, 24 और 60 से विभाजित किया जाय तो शेषफल क्रमशः 12, 17, 21 तथा 57 प्राप्त हों ।

  1. 999957

  2. 999963

  3. 999953

  4. 999967

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A Correct answer
Explanation

LCM of (15-12), (20-17), (24-21), (60-57) = LCM(3,3,3,3) = 3. Largest 6-digit multiple of 3 is 999999. Subtracting 3 gives 999996, but checking remainders: 999996 % 15 = 6 (we need 12), so add 9 to get 999957 which satisfies all conditions.