Its actually not hard at all.
If you reduce each number to their prime factorization you will see that you are forced into certain combinations.
For example, each one of the product triplets must have a factor of both 7 and 5.
Furthermore if you break the numbers down to the smallest three, middle three, and biggest three, you'll convince yourself that the product triplets must contain one from each group
Anyway, here is the answer:
They all equal 840.