The GCD of given numbers is 6.
Step 1 : Find prime factorization of each number.
$$\begin{aligned}18 =& 2\cdot3\cdot3\\[8pt]24 =& 2\cdot2\cdot2\cdot3\\[8pt]12 =& 2\cdot2\cdot3\\[8pt]\end{aligned}$$(view steps on how to factor 18, 24 and 12. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}18 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{3}}\cdot3\\[8pt]24 =& \color{blue}{\boxed{2}}\cdot2\cdot2\cdot\color{red}{\boxed{3}}\\[8pt]12 =& \color{blue}{\boxed{2}}\cdot2\cdot\color{red}{\boxed{3}}\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 2\cdot3 = 6 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.