question_answer 49)

Determine the smallest 3-digit number which is exactly divisible by 6, 8 and 12.

Answer:

                Firstly, we have to find out the LCM of 6, 8 and 12. 2 6,8,12 2 3,4,6 2 3,2,3 3 3,1,3 1,1,1 \[\therefore \] LCM\[=2\times 2\times 2\times 3=24\] We know that, smallest three digit number is \[\begin{align}   & 24)100(4 \\  & \,\,\,\,\,\,\,\,\frac{96}{4} \\ \end{align}\] On dividing 100 by 24,                            We find that, when 100 is divided by 24, we get remainder 4. Now, required three digit number which is exactly divisible by 24 = (Smallest 3-digit numbers + Divisor ? Remainder) = 100 + 24 ? 4 = 120