Final answer:
The least common denominator of the denominators 5, 2, and 3 is 30, which is the least common multiple of these numbers. It is the smallest number that each of the denominators divides into evenly.
Step-by-step explanation:
The least common denominator (LCD) of the denominators 5, 2, and 3 is the smallest number that each of the denominators can divide into without leaving a remainder. To find the LCD, we need to find the least common multiple (LCM) of these numbers. The multiples of 5 are 5, 10, 15, 20, 25, 30, and so on. The multiples of 2 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, and so on. Lastly, the multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, and so on. The smallest multiple that is common to all three lists is 30. Therefore, the least common denominator of 5, 2, and 3 is 30, which corresponds to option (a).