Common Denominator
The calculator converts 2, 3 or 4 fractions to the least common denominator: it finds the LCM of the denominators, the extra factors and the new fractions.
The common denominator calculator finds the least common denominator for two, three or four fractions, the extra factors, and rewrites the fractions with the new denominator.
Why you need a common denominator
Fractions can be added, subtracted and compared only when they have the same denominator. So fractions with different denominators are first converted to a common denominator — replaced by equal fractions that share one denominator.
How to find the least common denominator
- Find the least common multiple (LCM) of the denominators — this is the least common denominator.
- Find the extra factor for each fraction: divide the LCM by its denominator.
- Multiply the numerator and the denominator of each fraction by its extra factor.
Example. Find a common denominator for 3/4, 5/6 and 7/9.
4 = 22, 6 = 2 · 3, 9 = 32, LCM = 22 · 32 = 36.
Extra factors: 36 ÷ 4 = 9, 36 ÷ 6 = 6, 36 ÷ 9 = 4.
3/4 = 27/36, 5/6 = 30/36, 7/9 = 28/36
Quick ways to find the LCM of denominators
- If the largest denominator is divisible by the others, it is the common denominator: for 3 and 12 it is 12.
- If the denominators are coprime (no common divisors), the common denominator is their product: for 4 and 5 it is 20.
- Otherwise, factor the denominators into primes and take each prime with its highest exponent.
You can also simply use the product of the denominators, but the numbers get bigger and the answer will need simplifying later.