What is the least common multiple?
The smallest number that both inputs divide into evenly. The LCM of 4 and 6 is 12, because 12 is the first number in both times-tables.
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LCM (Least Common Multiple) calculator
Least common multiple of two positive integers.
lcm(a,b) = |a·b| / gcd(a,b)
A mind behind this: Euclid of Alexandria c. 300 BC
Frequently asked questions
How is the LCM calculated?
A reliable shortcut is LCM(a, b) = (a × b) / GCD(a, b). For 4 and 6: (4 × 6) / 2 = 12.
Where is this used in real life?
Adding fractions — the LCM of the denominators is the smallest common denominator. Scheduling — if one bus comes every 4 minutes and another every 6, they arrive together every 12 minutes (LCM of 4 and 6). Packaging — matching items sold in packs of different sizes so none are left over.
Why is the LCM useful for fractions specifically?
To add 1/4 and 1/6 you need a common denominator. The LCM of 4 and 6 is 12, so both become twelfths: 3/12 + 2/12 = 5/12 — using the smallest possible numbers.
What does the number line show?
Each row marks the multiples of one number. The LCM is the first point where a mark from both rows lines up.