6. Suppose $a , b , c$ are three positive integers. If 25 is the greatest common divisor of $a$ and $b$, and $3, 4, 14$ are all common divisors of $b$ and $c$, which of the following is correct?
(1) $c$ must be divisible by 56.
(2) $b \geq 2100$.
(3) If $a \leq 100$, then $a = 25$.
(4) The greatest common divisor of $a , b , c$ is a divisor of 25.
(5) The least common multiple of $a , b , c$ is greater than or equal to $25 \times 3 \times 4 \times 14$.