Question

Find the greatest number of 4 digits which is exactly divisible by 2,3,8,10

Answer 1

L.C.M of 8, 10, 12 = 2 x 2 x 2 x 3 x 5 =120.
We have to find the greatest 3 digit multiple of 120.
It can be seen that 120 x 8 =960 and120 x 9 =1080. Hence, the greatest 3- digit number exactly divisible by 8 , 10 and 12 is 960.

Answer 2

$Find\ the\ LCM\ of\ 2,\ 3,\ 8\ and\ 10. \\ \\ 2\ |\underline{2,\ 3,\ 8,\ 10} \\ 1\ |\underline{1,\ 3,\ 4,\ 5} \\ \\ \\ LCM = 2 \times 3 \times 4 \times 5 = 120 \\ \\ \\ The\ answer\ is\ the\ highest\ 4-digit\ multiple\ of\ 120. \\ \\ Largest\ 4-digit\ number\ is\ 9999. \\ \\ 9999\ divided\ by\ 120\ leaves\ quotient\ 83\ and\ remainder\ 39. \\ \\ \therefore\ \bold{83 \times 120 = 9960}\ is\ the\ greatest\ 4-digit\ number\ which\ is\ exactly \\ divisible\ by\ 2,\ 3,\ 8\ and\ 10.$

$Thank\ you. \\ \\ \\ \#adithyasajeevan$