4 Ways To Find The Least Common Denominator

Example: 1/2 + 1/3 + 1/5 Multiples of 2: 2 * 1 = 2; 2 * 2 = 4; 2 * 3 = 6; 2 * 4 = 8; 2 * 5 = 10; 2 * 6 = 12; 2 * 7 = 14; etc. Multiples of 3: 3 * 1 = 3; 3 * 2 = 6; 3 *3 = 9; 3 * 4 = 12; 3 * 5 = 15; 3 * 6 = 18; 3 * 7 = 21; etc. Multiples of 5: 5 * 1 = 5; 5 * 2 = 10; 5 * 3 = 15; 5 * 4 = 20; 5 * 5 = 25; 5 * 6 = 30; 5 * 7 = 35; etc.

Note that if no common multiple exists at this point, you may need to continue writing out multiples until you eventually come across a shared multiple. This method is easier to use when small numbers are present in the denominator. In this example, the denominators only share one multiple and it is 30: 2 * 15 = 30; 3 * 10 = 30; 5 * 6 = 30 The LCD = 30

Example: (15/15) * (1/2); (10/10) * (1/3); (6/6) * (1/5) New equation: 15/30 + 10/30 + 6/30

Example: 15/30 + 10/30 + 6/30 = 31/30 = 1 1/30

For example: 3/8 + 5/12. Factors of 8: 1, 2, 4, and 8 Factors of 12: 1, 2, 3, 4, 6, 12

In our example, 8 and 12 share the factors 1, 2, and 4. The greatest common factor is 4.

Continuing our example: 8 * 12 = 96

Example: 96 / 4 = 24

Example: 24 / 8 = 3; 24 / 12 = 2 (3/3) * (3/8) = 9/24; (2/2) * (5/12) = 10/24 9/24 + 10/24

Example: 9/24 + 10/24 = 19/24

Example: 1/4 + 1/5 + 1/12 Prime factorization of 4: 2 * 2 Prime factorization of 5: 5 Prime factorization of 12: 2 * 2 * 3

Example: There are two 2’s in 4; zero 2’s in 5; two 2’s in 12 There are zero 3’s in 4 and 5; one 3 in 12 There are zero 5’s in 4 and 12; one 5 in 5

Example: The largest count of 2 is two; the largest of 3 is one; the largest of 5 is one

Example: 2, 2, 3, 5

Example: 2 * 2 * 3 * 5 = 60 LCD = 60

Example: 60/4 = 15; 60/5 = 12; 60/12 = 5 15 * (1/4) = 15/60; 12 * (1/5) = 12/60; 5 * (1/12) = 5/60 15/60 + 12/60 + 5/60

Example: 15/60 + 12/60 + 5/60 = 32/60 = 8/15

Example: 8 + 2 1/4 + 2/3 8 = 8/1 2 1/4; 2 * 4 + 1 = 8 + 1 = 9; 9/4 Rewritten equation: 8/1 + 9/4 + 2/3

Note that you do not need to create a list of multiples for 1 since any number multiplied by 1 equals itself; in other words, every number is a multiple of 1. Example: 4 * 1 = 4; 4 * 2 = 8; 4 * 3 = 12; 4 * 4 = 16; etc. 3 * 1 = 3; 3 * 2 = 6; 3 * 3 = 9; 3 * 4 = 12; etc. The LCD = 12

Example: (12/12) * (8/1) = 96/12; (3/3) * (9/4) = 27/12; (4/4) * (2/3) = 8/12 96/12 + 27/12 + 8/12

Example: 96/12 + 27/12 + 8/12 = 131/12 = 10 11/12