4. It is known that construction teams A and B each have several workers. If team A lends 90 workers to team B, then the total number of workers in team B will be twice that of team A; if team B lends several workers to team A, then the total number of workers in team A will be six times that of team B. The original minimum number of workers in team A is
Answer 153.
Let the original number of workers in team A be $a$, and in team B be $b$. Suppose team B lends $c$ workers to team A. According to the problem, we have
$$
\begin{array}{c}
2(a-90)=b+90 \\
a+c=6(b-c)
\end{array}
$$
1
2
From equation 1, we get
$$
b=2 a-270
$$
3
Substituting equation 3 into equation 2, we get $c=\frac{11 a-1620}{7}=a-232+\frac{4(a+1)}{7}$.
Since $c \geq 1$, it follows that $a \geq 148$. Given $7 \mid 4(a+1)$, and $(4,7)=1$, then $7 \mid(a+1)$.
Therefore, the minimum value of $a$ is 153.