What is the value of (7)/(8) - (1)/(6)?

In a division $A \div B = C$ with remainder $R$, $A$ is the dividend, $B$ is the divisor, $C$ is the quotient, and $R$ is the remainder.

The number that divides the dividend (259) is 12.
The divisor is $\boxed{\text{12}}$.

Multiples of 8: $8, 16, \textbf{24}, 32, \dots$
Multiples of 6: $6, 12, 18, \textbf{24}, 30, \dots$
The LCM of 8 and 6 is 24.

For $\frac{7}{8}$:

For $\frac{1}{6}$:

The value is $\boxed{\frac{17}{24}}$.

Multiples of 18: $18, 36, 54, \textbf{72}, 90, \dots$

Multiples of 24: $24, 48, \textbf{72}, 96, \dots$

The least common multiple (LCM) of 18 and 24 is 72.
The least common multiple of 18 and 24 is $\boxed{\text{72}}$.