question_answer 1)

Find the smallest 4-digit number which is divisible ay 18, 24 and 32.

Answer:

                First, we have to find out the LCM of 18, 24, and 32. \[\therefore \] LCM \[=2\times 2\times 2\times 2\times 2\times 3\times 3=288\] We know that, smallest 4-digit number is On dividing 1000 by 288 \[\begin{align}   & 288\overline{)1000(}3 \\  & \,\,\,\,\,\,\,\,\,\,\,\,\frac{864}{136} \\ \end{align}\] 2 18, 24, 32 2 9, 12, 16 2 9, 6, 8 2 9, 3, 4 2 9, 3, 2 3 9, 3, 1 3 3, 1, 1 1, 1, 1 When we divide 1000 by 288, we get 136 as remainder. \[\therefore \] Required smallest 4-digit number which is exactly divisible by 18, 24 and 32 = (Smallest 4-digit number + Divisor - Remainder) = 1000 + 288 ? 136 = 1152