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(B) To find the greatest four-digit number divisible by $24, 28, 30$,and $35$,we first calculate the $L.C.M.$ of these numbers.$\begin{array}{r|rrrr}

Vedclass · Accepted Answer

$9240$

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(B) To find the greatest four-digit number divisible by $24, 28, 30$,and $35$,we first calculate the $L.C.M.$ of these numbers.$\begin{array}{r|rrrr} 2 & 24, & 28, & 30, & 35 \ \hline 2 & 12, & 14, & 15, & 35 \ \hline 3 & 6, & 7, & 15, & 35 \ \hline 5 & 2, & 7, & 5, & 35 \ \hline 7 & 2, & 7, & 1, & 7 \ \hline & 2, & 1, & 1, & 1 \end{array}$$L.C.M. = 2 	imes 2 	imes 2 	imes 3 	imes 5 	imes 7 = 840$.The greatest four-digit number is $9999$.Divide $9999$ by $840$:$9999 \div 840 = 11$ with a remainder of $759$.To find the greatest four-digit number divisible by $840$,subtract the remainder from $9999$:$9999 - 759 = 9240$.Thus,the required number is $9240$.

Find the greatest number of four digits which is exactly divisible by $24, 28, 30$ and $35$.

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