Cartan's magic formula and geometric product

Question

Cartan's formula say's $L_X = d \circ i_X + i_X \circ d$ while in geometric algebra, we have $ab = a \cdot b + a \wedge b$. These formula's seem similar to me. Especially, because the first is about k-forms, which are dual to multivectors, which the second is about. Furthermore, we also have $d \circ d=0$, and $a \wedge a = 0$. Are these similarities just coincidences, or this there some connection between them?