Finding the GCD of Integers

Consider the three integers 12, 18, and 30. Determine which of the following statements accurately describes the greatest common divisor (GCD) of these numbers.

The GCD of a set of numbers is the largest positive integer that divides each of the numbers without leaving a remainder. First, find the prime factorizations of each integer:

12 can be factored as $2^2 \cdot 3$.

18 can be factored as $2 \cdot 3^2$.

30 can be factored as $2 \cdot 3 \cdot 5$.

Using these factorizations, determine the GCD by identifying the lowest power of each common prime factor.