# How to find the lowest common denominator

Denominator is the lower part of a vulgar faction. ie a fraction of the form a / b, where b is the denominator. A common denominator is a common multiple of all denominators of two or more vulgar fractions. In particular, the lowest common denominator or lowest common denominator (LCD) is important. The least common multiple of all denominators is called the lowest common denominator. There are several methods of finding the common denominator or the lowest common denominator.

## Find the lowest common denominator

Method 1.

Look at the fractions 1/2 and 1/3. The denominators are 2 and 3. To find the common denominator we need multiples of 2 and 3. List the multiples of 2 and 3 on two separate lines.

2 → 2,4,6,8,10,12,14,16 .... 3 → 3,6,9,12,15,18,21 ... ..

We can see that 6 and 12 are on both lines. Therefore, they are a multiple of 2 and 3. However, the smaller of the two is 6 and is known as the least common multiple of 2 and 3. 12 is also a multiple, but not the smallest. So 6 is the LCD of 2 and 3. Then we can write 1/2 and 1/3 as equivalent fractions with 6 in the denominator. This enables simple addition and subtraction of the two fractions.

1/2 = 3/6 and 1/3 = 2/6

Then 1/2 +1/3 = 3/6 + 2/6 = 5/6 and 1/2 - 1/3 = 3/6 - 2/6 = 1/6

Method 2.

The above procedure is inefficient when larger numbers are involved. Hence, we need to use prime factorization to get the common denominator.

Look at the fractions 1/7, 1/8, 1/18, and 1/42. (Obviously, finding the multiples of each denominator and choosing the common denominator will be more difficult than the previous one)

First, write the denominators as the product of their prime factors. (Any real number can be written as the product of prime numbers). Then we have,

7 = 1 × 7 8 = 2 × 2 × 218 = 2 × 3 × 3 42 = 2 × 3 × 7

Select the prime numbers present in the numbers. For the above examples, 1, 2, 3, and 7 are the prime numbers in the numbers above. Multiply these prime numbers up to the largest number that appears in each denominator (for example, 2 is used three times in 8; therefore the multiple should be three times 2. Likewise, 3 is used twice in 18; therefore the product should contain 3 twice)

The least common multiple of 7,8,18 and 42 is

= 1 × 2 × 2 × 2 × 3 × 3 × 7 = 504

Therefore, the lowest common denominator is 504 and 1/7, 1/8, 1/18 and 1/42 can be used as equivalent fractions 72/504, 63/504, 28/504, 12/504. can be specified 