Least common denominator calculator
Type two or more fractions separated by commas. You get the LCD, how it was built from prime factors, and every fraction rewritten over it — ready to add, subtract or compare.
- Break each denominator into prime factors.
4 = 2^2; 6 = 2 × 3; 8 = 2^3 - Take the highest power of every prime that appears, and multiply.
2^3 × 3 = 24 - Rewrite each fraction over the LCD.
1/4 = 6/24, 5/6 = 20/24, 3/8 = 9/24
Why use the least common denominator?
Any common denominator works for adding, but the least one keeps numbers small. Adding 5/6 + 3/8 over 48 (6 × 8) gives 40/48 + 18/48 = 58/48, which still needs simplifying to 29/24. Over the LCD, 24, it's 20/24 + 9/24 = 29/24 directly.
The listing method
For small numbers, list multiples of the biggest denominator and stop at the first one the others divide: multiples of 8 are 8, 16, 24… and 24 is divisible by 6. Done: LCD = 24.
The LCD is the least common multiple of the denominators. Put it to work in adding fractions or comparing fractions.
Questions people ask
What is the least common denominator?
The smallest number that every denominator in a group divides into evenly. It is the least common multiple (LCM) of the denominators. For 1/4 and 1/6 the LCD is 12.
How do you find the LCD?
List multiples of the largest denominator until one is divisible by the others, or take the prime factors of each denominator and multiply the highest power of each prime. 8 = 2³ and 6 = 2 × 3, so the LCD is 2³ × 3 = 24.
Is the LCD the same as multiplying the denominators?
Only when the denominators share no common factor (like 3 and 4 → 12). For 4 and 6, multiplying gives 24, but the LCD is 12.
What is the LCD of 3, 4 and 5?
60, because they share no factors: 3 × 4 × 5 = 60.