The perimeter of an equilateral triangle is given by the formula:
\[ \text{Perimeter} = 3 \times \ell \]
where \( \ell \) is the length of each side. Given that the perimeter is 72 centimeters, we can set up the equation:
\[ 3\ell = 72 \]
To solve for \( \ell \), divide both sides of the equation by 3:
\[ \ell = \frac{72}{3} \]
Calculating this gives:
\[ \ell = 24 \]
Thus, the length of each side of the triangle is \( \boxed{24} \) centimeters.