Final answer:
The least common denominator for the fractions y/15x and y²/35 is 105x, which combines all the prime factors of both denominators at their highest powers.
Step-by-step explanation:
To find the least common denominator (LCD) for the fractions y/15x and y²/35, we need to determine the least common multiple (LCM) of the two denominators, which are 15x and 35. The prime factorization of 15x is 3×5×x, and the prime factorization of 35 is 5×7. The LCD must include each prime factor at its highest power that appears in either factorization.
We combine these to get the LCD as 3×5×7×x, which simplifies to 105x. Thus, the LCD is 105x, as it contains all the prime factors of both denominators at the highest power present in either denominator.