What is the least common denominator of 1/6 and 5/8?

24 — the least common multiple of 6 and 8. Rewritten over it, 1/6 becomes 4/24 and 5/8 becomes 15/24.

What's the difference between LCD and LCM?

None mathematically. LCM (least common multiple) is the general term for the smallest shared multiple; LCD (least common denominator) is that same number when it's serving as a denominator for fractions.

Why not just multiply the denominators?

That gives a common denominator, not always the smallest. For 6 and 8 the product is 48, but the LCD is 24 — the product forces bigger numbers and extra simplifying at the end.

How do I compute the LCD by hand?

LCD = (denom A × denom B) ÷ gcd(A, B). For 6 and 8: gcd is 2, so LCD = 48 ÷ 2 = 24.

Do I have to use the LCD to add fractions?

No — any common denominator works and gives the same final answer once simplified. The LCD just keeps the numbers smallest along the way.

How do I rescale each numerator to the LCD?

Divide the LCD by the fraction's original denominator, then multiply its numerator by that factor. 5/8 to twenty-fourths: 24 ÷ 8 = 3, so 5 × 3 = 15, giving 15/24.

Least Common Denominator Calculator

Fractions can only be added or subtracted when they share a denominator. The least common denominator is the smallest one that works for both — using it keeps every number in the calculation as small as possible, which means less simplifying at the end.

The LCD formula

Then each numerator is rescaled by the factor that lifts its denominator to the LCD:

Worked example

The calculator’s defaults are 1/6 and 5/8.

Both fractions now sit over 24 and can be added or subtracted directly.

Least Common Denominator Calculator worked example diagram — A visual read of the worked example above — the same numbers the calculator returns for its default inputs.

What your results mean

The least common denominator is the smallest shared denominator both fractions can use. The two new numerator values are what each original fraction’s numerator becomes once its fraction is rewritten over that shared denominator — the fractions’ values haven’t changed, only how they’re expressed.

Once both fractions share the LCD, adding or subtracting them is as simple as combining the numerators, since the denominators already match.

Common denominator pairs

Denominators	GCD	LCD
3, 4	1	12
4, 6	2	12
6, 8	2	24
6, 9	3	18
5, 10	5	10

Notice the LCD isn’t always the two denominators multiplied together — when they share a factor (like 6 and 8, which share a factor of 2, or 6 and 9, sharing a factor of 3), the LCD comes out smaller than that product.

For the full addition or subtraction after finding the LCD, use the adding fractions calculator or subtracting fractions calculator directly — both find the LCD automatically as part of the calculation.

Three ways to find the LCD by hand

List the multiples. Write out multiples of each denominator until one shows up in both lists. For 6 and 8: 6, 12, 18, 24 and 8, 16, 24. It’s quick for small numbers and slow for anything past about 20.

Use prime factors. Break each denominator into primes, then take the highest power of every prime that appears. Here and , so the LCD is . This is the method that scales best to three or more fractions.

Use the GCD. Divide the product of the denominators by their greatest common divisor, which is what the formula above does. It’s the fastest route when you can spot the GCD at a glance.

When one denominator divides the other

If the larger denominator is already a multiple of the smaller one, it is the LCD. For and , 12 is a multiple of 4, so the LCD is 12 and only the first fraction needs rewriting: . Spotting this saves a step every time.

Finding the LCD of three fractions

The calculator works with two fractions, but the idea extends. Take , and :

Rewritten over 60 they become , and , which add to . You can get the same LCD with the calculator in two passes: the LCD of 4 and 6 is 12, then the LCD of 12 and 10 is 60.

Common mistakes

Multiplying the denominators and calling it the LCD. is a common denominator, but not the least one.
Changing the denominator without the numerator. Turning into changes its value. Multiply top and bottom by the same factor, 4.
Using the GCD instead. The GCD of 6 and 8 is 2, which neither fraction can be rewritten over. The LCD is a multiple of both denominators, not a divisor.
Skipping a quick simplification. and have LCD 12, but simplifying to first drops the LCD to 6.

The LCD with algebraic fractions

The same idea works with variables. Factor each denominator and take every factor the highest number of times it appears:

and : the LCD is .
and : nothing is shared, so the LCD is .
and : the LCD is .

That’s the step that makes adding rational expressions possible, covered in the rational expressions lesson.

Try these

Fractions	LCD
1/4 and 1/10	20
2/9 and 5/12	36
3/8 and 7/20	40
1/6 and 1/15	30
5/14 and 3/21	42

About the formula: The LCD is the least common multiple (LCM) of the two denominators. Multiplying each fraction's numerator by whatever factor scales its denominator up to the LCD keeps the fraction's value unchanged.