Determine the smallest $$3$$-digit number which is exactly divisible by $$6, 8$$ and $$12$$.
Smallest number exactly divisible by $$6,8$$ and $$12$$
$$=$$LCM of $$6, 8, 12=24$$
We have to find the smallest $$3$$-digit multiple of $$24$$.
It can be seen that $$24\times 4=96$$ and $$24\times 5=120$$.
Hence, the smallest $$3$$-digit number which is exactly divisible by $$6, 8$$ and $$12$$ is $$120$$.