Final answer:
The least common multiple of the denominators 2/3 and 3/2 is 6, obtained by multiplying the denominators together since they have no common factors other than 1.
Step-by-step explanation:
The question asks for the least common multiple (LCM) of the denominators of the fractions 2/3 and 3/2. To find the LCM of two numbers, you need to find the smallest number that both denominators can divide into without leaving a remainder. In this case, the denominators are 3 and 2. You can list the multiples of these numbers (Multiples of 3: 3, 6, 9, 12...; Multiples of 2: 2, 4, 6, 8...) or you can use the fact that the LCM of two numbers can also be found by their product divided by their greatest common divisor (GCD), although for prime numbers like 2 and 3, their GCD is 1, so the LCM is just their product.
In this case, multiplying the denominators 3 and 2 gives us 6, which is indeed the LCM because it is the smallest number that both 3 and 2 can divide into evenly. Thus, the least common multiple of the two denominators 2/3 and 3/2 is 6.