How to find the lowest common denominator

Here is how to find out LCD of any two fractions; for example 1/3 and 1/6:

Their denominators are 3 and 6 and the multiples of 3 and 6 are

List the multiples of 3: 3, 6, 9, 12, 15, 18, 21, ...

List the multiples of 6: 6, 12, 18, 24, ...

The common multiples are 6, 12, 18 ... The least among these common multiples is 6. So, 6 is the Least Common Denominator of 1/3 and 1/6.

Formula 2:

Here is how to find out LCD of any two fractions; for example 1/8 and 7/12:

The denominators of the fractions are 8 and 12

Their prime factorizations are

8 = 2 * 2 * 2

12 = 2 * 2 * 3

The most occurrences of the primes 2 and 3 are 2 * 2 * 2 (in 8) and 3 (in 12).

Their product is 2 * 2 * 2 * 3 = 24

So, 24 is the LCD of these two fractions.