Final answer:
The least common denominator (LCD) of 9/10 and 1/7 is 70, found by multiplying the denominators together since they have no common factors other than 1.
Step-by-step explanation:
To find the least common denominator (LCD) of 9/10 and 1/7, we need to find the smallest number that both denominators (10 and 7) will divide into evenly. The denominators 10 and 7 are both prime with respect to each other, which means they have no common factors other than 1. Therefore, the least common denominator can be found by simply multiplying the two denominators together.
To calculate the LCD of 9/10 and 1/7:
Multiply the denominators: 10 * 7 = 70.
Confirm that both original denominators divide evenly into 70: 70 ÷ 10 = 7 and 70 ÷ 7 = 10.
Hence, the least common denominator of 9/10 and 1/7 is 70.