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Q. The least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder is

  • (A) 3363
  • (B) 2523
  • (C) 1683
  • (D) 1677
  • Correct Answer - Option(C)
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  • Filed under category Math
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Explanation by: Admin

The LCM of 5, 6, 7 and 8 = 840

∴ Required number = 840 k + 3 which is exactly divisible by 9 for some value of k.

Now, 840 k + 3 = 93 × 9 k + (3k + 3)

When k = 2, 3k + 3 = 9, which is divisible by 9.

∴ Required number = 840 × 2 + 3 = 1683

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