elementary number theory - How to use the Chinese Remainder theorem to solve a system of congruences

In my class the exact test of the Chinese Remainder Theorem we learned stated
$$\begin{align*} x &\equiv a_1 \pmod{n_1}\\ x &\equiv a_2 \pmod{n_2}\\ ...\\ x &\equiv a_L \pmod{n_L}. \end{align*}$$
has a unique solution modulo the product $n_1n_2...n_L$ if all the $n$'s are pairwise relatively prime.

How does this help us solve the following question. Other sources say to use a product $M$ along with $M_1,M_2,...$ all of which are absent in the text of my CRT

Find the smallest positive integer $x$ so that
$$\begin{align*} x &\equiv 3 \pmod{7}\\ x &\equiv 12 \pmod{11}\\ x &\equiv 5 \pmod{13}. \end{align*}$$