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Least Common Denominator (LCD) Calculator

Instantly find the LCD for up to 10 fractions. Compares Listing Multiples, Prime Factorization, and GCD methods. Rewrites fractions for easy addition/subtraction.

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About

Adding or subtracting fractions with different bottoms (denominators) requires finding a common ground. This number is the Least Common Denominator (LCD). Without it, combining 13 and 14 is impossible.

This tool does more than just output a number. It calculates the LCD using three distinct algorithms: Listing Multiples (visual), Prime Factorization (analytical), and the Euclidean GCD method (computational). It automatically reformats your input fractions with the new denominator, saving you the manual conversion step.

fractions common denominator LCD LCM math homework

Formulas

The LCD is essentially the Least Common Multiple (LCM) of the denominators. For two numbers a and b, it can be calculated using the Greatest Common Divisor (GCD):

lcm(a, b) = |a × b|gcd(a, b)

Reference Data

Input DenominatorsLCDMultiples Logic
2, 36Multiples of 2: 2, 4, 6... Multiples of 3: 3, 6...
4, 520GCD(4,5) is 1. LCD = 4×5
6, 8246, 12, 18, 24... vs 8, 16, 24...
3, 999 is a multiple of 3.
10, 1260Prime Factors: 2×5 vs 2×2×3

Frequently Asked Questions

They are mathematically the same concept applied in different contexts. LCM (Least Common Multiple) applies to any set of integers. LCD (Least Common Denominator) specifically refers to the LCM of the bottom numbers (denominators) of fractions.
Yes. To find the LCD of 3 or more numbers, you calculate the LCM of the first two, then take that result and find the LCM with the third number, and so on.
You cannot add or subtract fractions unless they share the same denominator. The LCD allows you to convert fractions into equivalent forms that can be combined.