Five pairwise products

You have four positive reals. They have six pairwise products. Five of them are $2,3,4,5,6$. What is the sixth one?

(Pairwise products of $a,b,c,d$ are $ab,ac,ad,bc,bd,cd$)




Solution (highlight to view):


Out of the given 5 products we must have that 4 of them are such that product of two is same as the product of the other two which is also the same as the product of the 4 unknown numbers. Moreover, the 6th missing product is this product divided by the 5th given product.

The only possibility with the given 5 products is $3 \times 4  = 2 \times 6$ and so the missing product is $\frac{12}{5}$.