Final answer:
The LCD of fractions with the denominators 7, 16, and 8 is 112, since 112 is the smallest number that 7, 16, and 8 all divide into evenly.
Step-by-step explanation:
The student is trying to find the least common denominator (LCD) of fractions with denominators 7, 16, and 8. Since 7 is a prime number and does not factor into 16 or 8, we can find the LCD by looking for a number that both 16 and 8 divide evenly into, which is 16, and then multiplying by 7 to incorporate the third denominator. Therefore, the LCD of fractions with denominators 7, 16, and 8 is 7×16, or 112.
To find the least common denominator (LCD) when one denominator is a prime number, we need to multiply the two non-prime denominators together. In this case, the non-prime denominators are 16 and 8, so the LCD would be 16 * 8 = 128.