Final answer:
The lowest common denominator of the fractions 3/8x and 5/18x is 72x, which is found by taking the least common multiple of 8 and 18 and including the variable x.
Step-by-step explanation:
To find the lowest common denominator (LCD) of the fractions 3/8x and 5/18x, we need to find the least common multiple (LCM) of the denominators. Since one denominator is 8x and the other is 18x, we are looking for the LCM of 8 and 18, after taking into consideration the variable part x. Both numbers have factors of 2, but 18 also has a factor of 3 that needs to be accounted for.
To find the LCM, we list the prime factors of each number:
8 = 23
18 = 2 × 32
We take the highest powers of the prime factors found in both numbers, thus the LCM of 8 and 18 is 23 × 32 = 72. Since we have the variable x in both denominators, we include it in the LCM to get the LCD, which is 72x.
This means that to combine the fractions, convert them both to have a denominator of 72x. This does not affect the variables in the numerator, as we are only finding a common denominator for addition or subtraction.