question_answer 50)

Determine the greatest 3-digit number exactly divisible by 8, 10 and 12.

Answer:

                Firstly, we have to find out the LCM of 8, 10 and 12. 2 8, 10, 12 2 4, 5, 6 2 2, 5, 3 3 1, 5, 3 5 1, 5, 1 1, 1, 1 \[\begin{align}   & 120\overline{)900(}8 \\  & \,\,\,\,\,\,\,\,\frac{960}{39} \\ \end{align}\] \[\therefore \] LCM \[=2\times 2\times 2\times 3\times 5=120\] We know that, largest 3-digit number = 999 On dividing 999 by 120. We find that, when 999 is divided by 120, we get remainder 39. Now, required three digit number which is exactly divisible by 120 = (Greatest 3-digit number - Remainder) = 999 ? 39 = 960