The lowest common denominator (LCD) is the smallest number that can serve as a common multiple of the denominators of two or more fractions. In the case of the numbers 8 and 9, we are looking for the least common multiple (LCM), which will also act as the LCD when dealing with fractions.
To find the LCM, we can use the prime factorization method. First, we need to determine the prime factors of both numbers:
- 8 can be factored into primes as: 2 × 2 × 2 (or 23).
- 9 can be factored into primes as: 3 × 3 (or 32).
The next step is to take the highest power of each prime number that appears in the factorizations of both numbers:
- For the prime number 2, the highest power from 8 is 23.
- For the prime number 3, the highest power from 9 is 32.
Now, we can calculate the LCM by multiplying these together:
LCM = 23 × 32 = 8 × 9 = 72.
Thus, the lowest common denominator (LCD) of 8 and 9 is 72. This means that if you have fractions with these denominators, you would use 72 as the common denominator to perform any addition or subtraction operations.