Question

Determine the smallest $3$-digit number which is exactly divisible by $5,8$ and $12.$

Answer 1

The smallest number which is divisible by $5,8$ and $12$ is the LCM of these numbers.

Now,

$5=5^1$

$8=2^3$

$12=2^2\times 3^1$

LCM $=2^3\times 3^1\times 5^1$

$=120$

$120$ is the smallest number which is divisible by $5,8$ and $12$ and also a $3-$digit number.

So, the answer is $120$