Least Common Denominator (LCD) — the 80/20
The LCD is just the LCM of all denominators. Use it to align fractions so you can add, subtract, or compare cleanly.
How it works
- List denominators and factor each into primes.
- Take the highest power of every prime across the set.
- Multiply those primes → LCD. Convert each fraction to denominator = LCD.
Sanity checks
- LCD ≥ largest denominator.
- If a denominator divides another, the LCD is the larger one.
- Coprime denominators → LCD is their product.
Shortcuts
- Two numbers: LCD = |a·b| / gcd(a,b).
- Build up for many numbers: fold with lcm(lcd, next).
- Scan for obvious multiples before factoring.
Pitfalls
- Mixing up LCD (for denominators) with GCD (for simplifying).
- Using the product of denominators when a smaller LCD exists.
- Forgetting to convert every fraction to the LCD.
Micro‑examples
- 4 and 6 → LCM 12 → LCD 12 → 1/4 → 3/12; 1/6 → 2/12.
- 12 and 18 → 2²·3 vs 2·3² → LCD 2²·3² = 36.
- 3, 5, 7 (coprime) → LCD 105.
Mini‑FAQ
- Is LCD different from LCM? LCD is the LCM of denominators.
- Do I need LCD to add? Any common denominator works; LCD keeps numbers smallest.
- Single fraction? Its denominator is the LCD.
Action tip
Enter fractions above; the tool finds the LCD, converts each to an equivalent form, and shows steps transparently.