Question

The smallest four digit number which is divisible by $18,24and32,$is

• A. $432$
• B. $768$
• C. $576$
• D. $1152$

Answer 1

The correct option is D

$1152$

Step -1: Find the LCM of $18,24and32,$

Factor of $18=2\times 3\times 3$

Factor of $24=2\times 2\times 2\times 3$

Factor of $32=2\times 2\times 2\times 2\times 2$

LCM of $18,24and32$$=2\times 2\times 2\times 2\times 2\times 3\times 3=288$

Step -2: For finding the four digit number

Four digit multiples of $288$ which is divisible by it

$\Rightarrow 288\times 2=576$

$\Rightarrow 288\times 3=864$

$\Rightarrow 288\times 4=1152$

Hence, the smallest four digit number which is divisible by $18,24and32,$is $1152$.