To find the LCM (Least Common Multiple) of fractions, we need to find the LCM of their denominators.

The given fractions are:
1) 3/8
2) 9/32
3) 33/48
4) 18/72

Step 1: Simplify the fractions
Let's simplify the fractions to their lowest terms before finding the LCM.

1) 3/8
This fraction is already in its simplest form.

2) 9/32
To simplify this fraction, we can divide both the numerator and denominator by the greatest common divisor (GCD) of 9 and 32, which is 1.
9 ÷ 1 = 9
32 ÷ 1 = 32
So, the simplified fraction is 9/32.

3) 33/48
To simplify this fraction, we can divide both the numerator and denominator by their GCD, which is 3.
33 ÷ 3 = 11
48 ÷ 3 = 16
So, the simplified fraction is 11/16.

4) 18/72
To simplify this fraction, we can divide both the numerator and denominator by their GCD, which is 18.
18 ÷ 18 = 1
72 ÷ 18 = 4
So, the simplified fraction is 1/4.

Step 2: Find the LCM of the denominators
Now that we have simplified the fractions, we need to find the LCM of the denominators: 8, 32, 48, and 72.

The prime factorization of these numbers is as follows:
8 = 2^3
32 = 2^5
48 = 2^4 * 3
72 = 2^3 * 3^2

To find the LCM, we need to take the highest power of each prime factor that appears in any of the numbers.

The LCM of the denominators is:
2^5 * 3^2 = 32 * 9 = 288

Step 3: Convert the LCM to a fraction with the same denominator
Since the LCM is 288, we need to convert it to a fraction with the denominator 288.

1) 3/8 = (3 * 36)/(8 * 36) = 108/288
2) 9/32 = (9 * 9)/(32 * 9) = 81/288
3) 11/16 = (11 * 18)/(16 * 18) = 198/288
4) 1/4 = (1 * 72)/(4 * 72) = 72/288

Step 4: Determine the LCM of the fractions
Now that all the fractions have the same denominator, we can find the LCM by taking the maximum numerator of the fractions.

In this case, the maximum numerator is 198, so the LCM is 198/288.

Therefore, the correct answer is option C) 198/8.