Find the Least Common Multiple (LCM) of two or more integers using prime factorization. Also shows GCF and step-by-step prime factor method.
| Number | 2 | 3 | 5 | Factors |
|---|---|---|---|---|
| 4 | 2^2 | — | — | 2^2 |
| 6 | 2 | 3 | — | 2 × 3 |
| 10 | 2 | — | 5 | 2 × 5 |
| LCM (max) | 2^2 | 3 | 5 | 2^2 × 3 × 5 |
For multiple numbers, LCM is computed iteratively.
| Step | Calculation | Result |
|---|---|---|
| 1 | LCM(4, 6) | 12 |
| 2 | LCM(12, 10) | 60 |
| Property | Formula |
|---|---|
| LCM from GCF | LCM(a,b) = a×b / GCF(a,b) |
| Prime factorization | Take highest power of each prime |
| Relationship | GCF × LCM = a × b |
| LCM ≥ max(nums) | Always true |
| If GCF = 1 | LCM = a × b |
| Numbers | LCM | Use case |
|---|---|---|
| 2, 3 | 6 | Adding ½, ⅓, ⅙ |
| 4, 6 | 12 | Adding ¼, ⅙ |
| 3, 4 | 12 | Adding ⅓, ¼ |
| 6, 10 | 30 | Adding ⅙, 1/10 |
| 5, 7 | 35 | Adding ⅕, 1/7 |