LCM Calculator
Find the Least Common Multiple (LCM) of two or more numbers.
When two cycles line up again
The least common multiple is the smallest number both values divide into exactly. It answers questions about repeating cycles coinciding: buses leaving every 12 and 18 minutes depart together every 36 minutes, because 36 is the LCM. That is the intuition worth carrying — the LCM is when two rhythms next align.
Prime factorisation gives it directly: take every prime appearing in either number, at the highest power it reaches in either. For 12 (2² × 3) and 18 (2 × 3²), that is2² × 3² = 36. The faster route uses the GCF identity: LCM(a,b) = (a × b) / GCF(a,b), and since the Euclidean algorithm finds a GCF in a few steps, this handles large numbers easily.
The everyday use is adding fractions, where the lowest common denominator is exactly the LCM of the denominators. Using any common multiple works, but the lowest one keeps the arithmetic small and leaves less to simplify at the end. For more than two numbers, take the LCM of the first pair, then the LCM of that result with the next, and so on.
Frequently Asked Questions
What is the Least Common Multiple (LCM)?
The LCM of two or more integers is the smallest positive integer that is evenly divisible by all numbers in the set.
How is LCM calculated using GCD?
LCM(a, b) = |a × b| / GCD(a, b).
How do I find the least common multiple?
Either list multiples until one matches, or use prime factorisation and take the highest power of each prime. The fastest method uses the GCF: LCM(a,b) = (a x b) / GCF(a,b), which avoids factorising large numbers.
What is the LCM used for?
Adding fractions with different denominators, where the LCM is the least common denominator; scheduling problems such as when two events with different cycles coincide; and gear ratios. It is the natural answer to 'when will these two repeating patterns line up again'.