If each of the three nonzero numbers a, $b$ and $c$ is divisible by 3, then abc must be divisible by which one of the following the numbers?

Step 1 (Formulate Divisibility): We are given that each of the three nonzero numbers $a$, $b$, and $c$ is divisible by $3$. By definition, there exist non-zero integers $k_1,k_2,k_3$ such that:

Step 2 (Compute the product abc): Multiplying the three equations:

Since $k_1,k_2,k_3$ are integers, their product $k_1{k}_2{k}_3$ is also an integer. Therefore, by definition of divisibility, the product $abc$ must be divisible by 27.

Step 3 (Conclusion): The product $abc$ is divisible by 27.