The least common denominator (LCD), also known as the lowest common denominator, is the smallest number that can be a common denominator for a set of fractions.
The LCD of two fractions, then, is the least common multiple of the denominators of the two fractions. Therefore, it would help if you first found the least common multiple of the two fractions’ denominators to find the LCD of the two fractions.
How to Find the LCD of Two Fractions?
While finding the least common denominator can seem complicated, it is a straightforward process. You can use two methods to find the LCD of two fractions.
Method 1
The first method finds the least common denominator of two fractions by figuring out the lowest possible common denominators.
For example:
Find the least common denominator of 1/4 and 1/6:
The denominators of these two fractions are 4 and 6. The multiples of 4 and 6 are:
Multiples of 4:4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48
Multiples of 6:6, 12, 18, 24, 30, 36, 42, 48, 54, 60
From this list of multiples, we can see that the least common multiple is 12. So, the least common denominator of these two fractions is 12.
Answer: The least common denominator of 1/4 and 1/6 is 12.
Method 2
To find the least common denominator using the second method, you must find the prime factors of the denominators. The second method of finding the LCD of two fractions can be laid out in these four easy steps:
- Factor each of the denominators into its primes.
- List all of the primes, noting down all of the matching primes.
- Multiply the factors, and the product will be the lowest common multiple of the denominators.
- The lowest common multiple of the denominators is the LCD of the two fractions.
For example:
Find the least common denominator of 1/8 and 1/12:
The denominators of these fractions are 8 and 12.
Now, we have to find the prime factorizations of these two denominators:
Prime factorisations of 8= 2 × 2 × 2
Prime factorisations of 12= 2 × 2 × 3
The most occurrences of the prime numbers 2 and 3 are two × 2 × 2 in 8 and 3 in 12.
Now we have to multiply all of the factors together.
2 × 2 × 2 × 3 = 24
Answer: The least common denominator of 1/8 and 1/12 is 24.
