Question

Determine two numbers nearest to $10000$ which are exactly divisible by each of the numbers $20,24and35$.

Answer 1

Step 1 : Find the LCM of the given numbers

$2$	$20,24,35$
$2$	$10,12,35$
$5$	$5,6,35$
	$1,6,7$

LCM of $20,24and35$ is $2\times 2\times 5\times 1\times 6\times 7=840$

Step 2 : Divide $10000$ by the LCM i.e $840$

$$\begin{gathered} 840\overline{)10000}\overline{)11} \\ \underline{-840} \\ 1600 \\ \underline{-840} \\ 760 \end{gathered}$$

Step 3 : Now one number nearest to $10000$ can be found by adding the difference of $840and760$ which is $80$ to $10000$

which is $10000+80=10080$.

other number can be obtained by subtracting the remainder from $10000$, which is $10000-760=9240$

Hence two numbers nearest to $10000$ which are divisible by $20,24and35$ are $9240and10080$