, 2019

We say that a number is a child of another number if we can get it by placing between any two digits of the other number either nothing, a $+$, or a $\times$. For example, $145$ and $5$ are children of $12121$ because $145 = 12 \times 12 + 1$ and $5 = 1 + 2 \times 1 + 2 \times 1$. The number $15$ is both a child of $12121$ and of $33333$, because $12 + 1 + 2 \times 1 = 15 = 3 + 3 + 3 + 3 + 3$.
Which of the following numbers is also a child of both $12121$ and $33333$?
A) $18$ B) $34$ C) $39$ D) $42$ E) $45$