Final answer:
The lowest common denominator for the fractions 1/3 and 5/7 is 21, calculated by multiplying the two prime denominators together.
Step-by-step explanation:
To find the lowest common denominator (LCD) for the fractions 1/3 and 5/7, we need to determine the smallest number that is a multiple of both denominators. In this case, the denominators are 3 and 7, which are both prime numbers. Therefore, the LCD is simply the product of these two numbers since they have no other common multiples besides 1.
The calculation of the LCD is as follows:
- LCD for 1/3 and 5/7 = 3 × 7
- LCD = 21
Thus, the lowest common denominator for 1/3 and 5/7 is 21.