Computing $\mathrm{lcm}(2,3,6)$

Question

I have the following question:

I will earn money if I share it with 2, 3 and 6 people. The money I am about to earn is less than $100,000 (USD). How much money will I earn if the condition is met?

I know that the possible results are $12, 42, 84$, but I can't find out why.

I am doing:

2 x 3 x 6

Which, defragmenting:

2 x 3 = 6

6 x 6 = 36

It is a (very) simple calculation, but my brain got stuck on it. I just can't understand why the possible solutions can be $12,42$, and/or $84$.

Could someone explain this one for me?

Answer 1

Hint: The LCM of $2,3,6$ is $6$, which you can verify easily. But presumably you will take a share, too, so we want the LCM of $3,4,7$. Now there is only one solution less than $100$.