LCD stands for least common denominator and LCM stands for least common multiple. The least common multiple is the smallest number that is divisible by all of the numbers in a set. The least common denominator is used when adding fractions so that you can add fractions with different denominators.

### Finding LCM

Find the prime factorization of each number in your set. The prime factorization is the prime numbers that must be multiplied together to get a particular number. For example, the prime factorization of 60 would be 2_2_3*5 because those are all prime numbers that equal 60 when multiplied.

Convert the prime factorization to exponential form. For example, 2_2_3_5 would become 2^2_3^1*5^1.

Compare the exponential forms and take the highest exponent for each prime number. For example, if your numbers were 60 and 72, the prime factorizations would be 2^2_3^1_5^1 and 2^1_3^2_4^1 and you would use 2^2_3^2_4^1*5^1, or 720. Therefore 720 would be your least common multiple because it is the smallest number divisible both 60 and 72.

### Using LCD

Determine the LCM of the denominators in the fractions that you are trying to add. For example, if you are adding 2/9 and 5/12, you would find the LCM of 9 and 12 and find the LCM to be 36. This number will be the least common denominator.

Divide the LCD found in step one by each of the denominators. For example, 36 divided by nine is four and 36 divided by 12 is three.

Multiply both the numerator and denominator by the number found in step two. For example, since 36 divided by nine is four, you would multiply both 2/9 by 4/4 and get 8/36. For 5/12, you would multiply by 3/3 and get 15/36.

Add the numerators of the newly found fractions from step three but keep the same denominator. For example, 8/36 plus 15/36 becomes 23/36.