LCM Calculator
Calculate the least common multiple (LCM) of two or more numbers. Uses prime factorization and division methods.
6 values
Mean (Average)
24
Median
18.5
Sum
144
Count
6
Min
8
Max
47
About the LCM Calculator
The Least Common Multiple (LCM) is the smallest positive integer divisible by all given numbers. LCM appears in fraction arithmetic (to find a common denominator), scheduling (to find when repeating events coincide), and engineering (gear ratios and synchronisation problems). Our LCM calculator handles two or more numbers and shows both the division method and prime factorisation approach.
Formula
LCM(a,b) = (a × b) ÷ GCF(a,b)
How It Works
Relationship between GCF and LCM: LCM(a,b) = a × b / GCF(a,b). For LCM(12, 18): GCF(12,18) = 6. LCM = 12 × 18 / 6 = 36. Verify: 36/12 = 3 ✓, 36/18 = 2 ✓. Prime factorisation method: take each prime factor at its highest power in either number. 12 = 2²×3, 18 = 2×3² → LCM = 2²×3² = 36.
Tips & Best Practices
- ✓LCM(a, b) ≥ max(a, b) — the LCM is always at least as large as the largest input.
- ✓Two gears with 12 and 18 teeth first realign after 36 teeth = LCM(12,18) rotations.
- ✓Add 1/12 + 1/18: LCD = LCM(12,18) = 36 → 3/36 + 2/36 = 5/36.
- ✓LCM of coprime numbers equals their product: LCM(7,9) = 63 because GCF(7,9) = 1.
- ✓Scheduling: if event A repeats every 4 days and event B every 6 days, they next coincide in LCM(4,6) = 12 days.
Who Uses This Calculator
Students adding fractions with unlike denominators, engineers synchronising periodic processes, musicians finding rhythmic coincidences in polyrhythms, programmers scheduling repeating tasks, and teachers demonstrating number theory all use LCM calculations.
Optimised for: USA · Canada · UK · Australia · Calculations run in your browser · No data stored
Frequently Asked Questions
What is LCM used for?
LCM is used to add fractions with different denominators. LCM(4,6) = 12, so 1/4 + 1/6 = 3/12 + 2/12 = 5/12.