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Find 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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Find 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 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

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