Equal products??

I ve got a logical approach...............

2 = 2 3 = 3 12 = 2 2 3 14 = 2 7 15 = 3 5 20 = 2 2 5 21 = 3*7

Total prime factors are 14 so 7 must be on one side and 7 on other. we observe that there are 6 - 2s , 4 - 3s, 2 - 7s and 2 - 5s. Hence in one set there would be 3 - 2s, 2 - 3s, 1 - 7 and 1- 5 so, the product of set is 2 2 2 3 3 7 5 = 2520

(2,3,20,21)----(12,14,15)

Let the product of each of the two sets be $x$ .

This means, the product of all the numbers in both sets would be $x^2$ .

Since we can already evaluate the product of all of the numbers (since we only don't know which set they're in), all we need to do is multiply all the numbers (to get $x^2$ ) and then take the square root to get $x$ .

Thus, the answer is $x=\sqrt{2\times 3\times 12\times 14\times 15\times 20\times 21} =2520$ .

Nice problem! :)