Factor the second denominator, then simplify:

The least common denominator is the least common multiple of the denominators of a set of fractions.

Simply multiply the two denominators together to find the LCD:

The denominators are 7, 3, and 9. We have to find the common multiple of 7, 3, and 9.

Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63

Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90

The least common multiple of the 3 denominators is 63.

In order to continue to simplify this problem, we will need to multiply both denominators together in order to simplify the numerators.

Multiply both of the denominators by using the FOIL method.

Simplify this expression.

The least common denominator required is:

Be careful not to continue and solve the problem!

The answer is:

Solution 1

The least common denominator is the least common multiple of the denominators.

We list the multiples of each denominator and we find the lowest common multiple.

Multiples of 19: 19, 38, 57, 76, 95, 114, 133, 152, 171, 190

Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100

The lowest common multiple in both lists is 95.

Solution 2

19 and 5 are prime numbers. They have no positive divisors other than 1 and themselves.

The least common denominator of two prime numbers is their product.

To find the least common denominator for these two fractions, multiply the denominators together.

To find the least common denominator for these two fractions, multiply the denominators together.

In order to determine the least common denominator, we will need to use the FOIL method to expand the denominators.

Multiply the terms.

Combine like-terms.

The answer is:

The least common denominator is the term that is both divisible by all denominators and do not have common denominators smaller than this term.

Notice that both denominators can share a . We can simply change the first denominator to by multiplying an x-term.

For the second denominator, notice that we can change the three to a nine, similar to the first denominator by multiplying a three.

Since these terms are common and is the least possible term, this is the least common denominator.

The answer is:

Determine the least common denominator by multiplying the denominators together.

Multiply the first two terms together.

Multiply this quantity with the third term.

Use the FOIL method to expand this expression.

Simplify and combine like terms.

The answer is: