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

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Solution

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 $120$

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