Step 1: Recall the three activation pathways. The complement system can be triggered by the classical pathway, the alternative pathway, and the lectin pathway.
Step 2: Trace the classical pathway. It starts with C1 binding antigen-antibody complexes, then activates C4 and C2 to form the C3 convertase C4b2a.
Step 3: Trace the alternative pathway. It is antibody independent and forms its own C3 convertase (C3bBb) without using C1, C4, or C2.
Step 4: Find the convergence. Both pathways generate a C3 convertase that cleaves C3 into C3a and C3b. From C3 onward (C3 to C5 to the membrane attack complex C5-C9), the cascade is identical. Therefore C3 is the first component shared by both pathways.
Answer: C3 (option C).