How Do You Find a Common Denominator and a Least Common Denominator?

LCD stands for Least Common Denominator
You can always find a common denominator by multiplying all the denominators together, but It's not always the LCD!
To find the LCD, you need to find the prime factors of every number, figure out the most times that each prime factor shows up, and then multiply the factors you find together!
So we multiply 3 factors of 2 by 1 factor of 3 to get the LCD!
Our LCD is 24!

1. Multiplying all the denominators together is a sure way to find a common denominator, but it won't necessarily find the Least common denominator!
1. Multiplying all the denominators together is a sure way to find a common denominator, but it won't necessarily find the Least common denominator!
2. 192 is a common denominator for our three fractions
1. Keep in mind that 2 is prime, but 4 is not!
2. We still have to factor 4 before we are done finding 8's primes
1. Keep in mind that 2 is prime, but 4 is not!
2. We still have to factor 4 before we are done finding 8's primes
3. The 2's are prime, so we are done factoring 8!
4. 8's prime factors are 2, 2, and 2
1. 2 and 3 are both prime, so 6's prime factors are just 2 and 3!
1. 2 appears 3 times in 8
2. 2 appears only 2 times in 4
3. And 2 appears only 1 times in 6
1. 3 does not appear in 8 and 4
2. So this means that the prime factors that occur most often are the three 2's and the one 3
1. Multiplying together the most common prime factors together
2. The least common denominator of one eighth, one fourth, and two sixths is 24!

Find the common denominator for these fractions:1/8, 1/4, 2/6