Question

The smallest 3-digit number which is completely divisible by 18, 24 and 32 is

• A. $576$
• B. $13824$
• C. $432$
• D. $288$

Answer 1

The correct option is D $288$

Note that the smallest 3-digit number which is completely divisible by 18, 24 and 32 is the LCM(Least Common Multiple) of the numbers 18, 24 and 32.Thus,
$\begin{array}{cc}2& 18,24,32\\ 3& 9,12,16\\ 2& 3,4,16\\ 2& 3,2,8\\ 2& 3,1,4\\ 2& 3,1,2\\ 3& 3,1,1\\ & 1,1,1\end{array}$
$⟹LCM=2\times 3\times 2\times 2\times 2\times 2\times 3=288$
Thus, the smallest 3-digit number which is completely divisible by 18, 24 and 32 is 288.