What is the least number which,when divided b | vedclass

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(C) First,find the $L.C.M.$ of $5, 6, 7, 8$.$5 = 5$$6 = 2 	imes 3$$7 = 7$$8 = 2^3$$L.C.M. = 5 	imes 3 	imes 7 	imes 8 = 840$.Any number that leave

Vedclass · Accepted Answer

$1683$

Vedclass · Answer

(C) First,find the $L.C.M.$ of $5, 6, 7, 8$.$5 = 5$$6 = 2 	imes 3$$7 = 7$$8 = 2^3$$L.C.M. = 5 	imes 3 	imes 7 	imes 8 = 840$.Any number that leaves a remainder of $3$ when divided by $5, 6, 7, 8$ is of the form $(840x + 3)$,where $x$ is a natural number.We are given that this number is divisible by $9$.So,$(840x + 3) \div 9$ must be an integer.$840x + 3 = (837x + 3x + 3) = 9(93x) + 3(x + 1)$.For this to be divisible by $9$,$(x + 1)$ must be a multiple of $3$.For the least number,let $x + 1 = 3$,which gives $x = 2$.Substituting $x = 2$ in $(840x + 3)$:Required number $= 840(2) + 3 = 1680 + 3 = 1683$.

What is the least number which,when divided by $5, 6, 7, 8$ gives the remainder $3$ but is divisible by $9$?

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