LCM Calculator — quick guide
1) Core idea
The least common multiple (LCM) of numbers is the smallest positive integer divisible by all of them. It’s vital for fraction addition, schedules, and periodic alignment.
2) How this tool works
- Two numbers: LCM(a,b) = |a·b| / GCD(a,b).
- Many numbers: reduces pairwise, i.e., LCM(a,b,c) = LCM(LCM(a,b), c).
- Also shows prime‑factor and division‑table methods for learning/verification.
3) Sanity checks
- LCM ≥ max(all inputs).
- For coprime a,b, LCM = a·b.
- Identity: LCM(a,b) × GCD(a,b) = a × b (two numbers).
4) Shortcuts that help
- Factor small numbers quickly with primes 2,3,5.
- If one divides the other, LCM is the larger number.
- Use highest prime powers across inputs when using factorization.
5) Common pitfalls
- Mixing up GCD powers (use highest for LCM, lowest for GCF).
- Forgetting to take absolute values with negative inputs in theory; this tool expects positive integers.
- Arithmetic overflow when multiplying first—prefer the formula with division by GCD.
6) Micro‑examples
- LCM(12, 18) = 36.
- LCM(4, 6, 8) = 24.
- LCM(5, 7) = 35 (coprime).
7) Mini‑FAQ
- LCM vs GCF? LCM is the least shared multiple; GCF is the greatest shared divisor.
- Zero allowed? Not in this tool; mathematically LCM with 0 is undefined or treated specially.
- Large inputs? The formula uses GCD first to avoid overflow.
8) Action tip
Find LCM to get a common denominator, add fractions, then simplify using the GCF tool.