What is the LCM?
The least common multiple of two or more integers is the smallest positive number that is a multiple of each of them. For 4 and 6, the multiples of 4 are 4, 8, 12, 16, 20, 24… and the multiples of 6 are 6, 12, 18, 24… — so the least shared one is 12.
You'll use LCM when adding fractions (common denominators), planning recurring schedules, or solving number-theory homework. It pairs with the GCD: for any two positives, LCM(a,b) × GCD(a,b) = a × b.
How this calculator works
1
GCD via Euclidean algorithmWe compute the greatest common divisor with repeated division — fast and exact, no guessing.
2
LCM from the identityFor each pair we use
LCM = |a·b| / GCD, then fold that result into the next number until the list is done.3
Prime-factor checkWe also factor each input so you can verify the answer the textbook way — take the highest power of every prime that appears.
Quick example: LCM(12, 18, 24).
12 = 22 × 3 · 18 = 2 × 32 · 24 = 23 × 3
Highest powers: 23 × 32 = 72
12 = 22 × 3 · 18 = 2 × 32 · 24 = 23 × 3
Highest powers: 23 × 32 = 72
When you'd actually need this
- Fractions: 1/12 + 5/18 needs denominator LCM(12,18) = 36.
- Schedules: Bus A every 12 min, Bus B every 18 — they meet every LCM minutes.
- Gear ratios / cycles: Any problem asking “when do these patterns next line up?â€
More walkthroughs: Worked Examples · Formula & Methods · How LCM Works.
