QA – Placement Quizzes | LCM | Question 12

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

(A) 1677

(B) 1683

(C) 2523

(D) 3363

Answer: (B)
Explanation: LCM of 5, 6, 7 and 8 = 840.
Therefore, required number is of the form 840y + 3.
Least value of y for which 840y+3 is divisible by 9 is 2.
For y=2, 840y+3 = 1683.

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