Answer: To rewrite the fractions 2/3 and 4/15 with the least common denominator (LCD), we need to find the smallest multiple that both denominators, 3 and 15, divide into evenly.
The prime factorization of 3 is 3, and the prime factorization of 15 is 3 * 5.
To find the LCD, we take the highest power of each prime factor that appears in either denominator. In this case, the highest power of 3 is 3, and the highest power of 5 is 5.
The LCD is the product of these highest powers: LCD = 3 * 5 = 15.
Now, we can rewrite the fractions with the least common denominator:
2/3 = (2/3) * (5/5) = 10/15
4/15 = (4/15) * (1/1) = 4/15
Therefore, the fractions 2/3 and 4/15 can be rewritten with the least common denominator as 10/15 and 4/15, respectively.
Explanation: