What is the least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder?
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L.C.M. of 5, 6, 7, 8 = 840.
Required number is of 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
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1683 is the least number which can be divided by 5 ,6 ,7, 8.
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