Final answer:
To find the lowest common multiple (LCM) of the denominators 5/9 and 3/15, simplify the fractions and find the LCM of the denominators.
Step-by-step explanation:
To find the lowest common multiple (LCM) of the denominators of the fractions 5/9 and 3/15, we need to first simplify the fractions. The first fraction, 5/9, cannot be simplified further. The second fraction, 3/15, can be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 3. This simplifies the fraction to 1/5.
Next, we need to find the LCM of the denominators, which are 9 and 5. The prime factorization of 9 is 3 x 3, and the prime factorization of 5 is 5. To find the LCM, we take the highest power of each prime factor that appears in either number, which gives us 3 x 3 x 5 = 45.
Therefore, the LCM of the denominators of the fractions 5/9 and 3/15 is 45.