Which is the greatest 5 digit number which when divided by 3 6 8 and 11 obtains the remainder 4 in each case?

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Hint: We know that the greatest 5 digit number is 99999, but we have to find the greatest 5 digits number that will give remainder of 5, when divided by 8 and 9 respectively. For this we take L.C.M of 8 and 9 and divide the number 99999.Complete step-by-step answer:We know that the greatest 5 digit number is 99999.Now, we have to find the greatest 5 digit number that will give a remainder of 5, when divided by 8 and 9 respectively.So, L.C.M of 8 and 9 is shown below: - \[\begin{align} & 8=2\times 2\times 2 \\ & 9=3\times 3 \\ \end{align}\]L.C.M = \[2\times 2\times 2\times 3\times 3=72\].Hence, the L.C.M of 8 and 9 is 72.Now, we will find the greatest 5 – digit number divisible by 8 and 9 by dividing 99999 by 72.The division of 99999 by 72 is shown as below: -\[72\overset{1388}{\overline{\left){\begin{align} & 99999 \\ & \underline{-72} \\ & 279 \\ & \underline{-216} \\ & 639 \\ & \underline{-576} \\ & 639 \\ & \underline{-576} \\ & 63 \\ \end{align}}\right.}}\]So, from the above division we get,Quotient = 1388Remainder = 63So, the greatest 5 – digit number divisible by 8 and 9 = 99999 – 63 = 99936.Required number = 99936 + 5 = 99941\[\because \] We have been given that a remainder of 5 is there when the number is divided by 8 and 9 respectively. So, we add the remainder to the number which is divisible by 8 and 9.Therefore, we get the greatest number of 5 digits, that will give a remainder of 5, when divided by 8 and 9 respectively is 99941.Note: Just be careful while doing calculation as there is a chance that you might make a mistake and you will get the incorrect answer. Most students make the mistake of adding the remainder to 99999 instead of subtracting it. Also, they may forget to add 5 to 99936 and often write 99936 as the final answer.