LCM Calculator
Compute the least common multiple of several integers with the working and prime factorisation
输入整数
支持输入多个正整数，至少需要 2 个数才能计算最小公倍数
About this tool
The LCM calculator finds the least common multiple of two or more integers:
- Any count: enter as many integers as you need
- Live result: computed as you type
- Working shown: the calculation uses LCM(a,b) = |a times b| / GCD(a,b) and displays each step
- Prime factorisation: every input number is broken into primes
What the LCM is
The least common multiple is the smallest positive integer that every number in the set divides. For example LCM(4, 6) = 12, because 12 is the smallest positive integer divisible by both 4 and 6.
When to use it
- Find the common denominator when adding fractions
- Number theory homework and study
- Solve periodic problems, such as when events with different cycles line up
- Synchronisation calculations in engineering
Math notes
- LCM formula: LCM(a,b) = |a times b| / GCD(a,b), so the GCD comes first
- More than two numbers: take the LCM of the first pair, then combine it with the next number, and so on
- Common denominators: the common denominator of fractions is the LCM of their denominators