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Problems on HCF and LCM - General Aptitude

Q1:

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 1677

B 1683

C 2523

D 3363

ANS:B - 1683

L.C.M. of 5, 6, 7, 8 = 840.  Required number is of the form 840k + 3 Least value of k for which (840k + 3) is divisible by 9 is k = 2.  Required number = (840 x 2 + 3) = 1683.