How it works
The least common multiple (LCM) is the smallest positive number that every number in the list divides evenly. For 4, 6 and 8 it is 24.
It is computed pairwise using the GCF: lcm(a, b) = a × b ÷ gcd(a, b), then combined with the next number. Big-integer arithmetic keeps the answer exact even for long lists.
The LCM of denominators is the least common denominator, which is what you need to add or subtract fractions.
Formula
lcm(a, b) = |a × b| ÷ gcd(a, b); lcm(a, b, c) = lcm(lcm(a, b), c)
Questions people ask
How do I find the LCM by hand?
Write the prime factorization of each number and take every prime at its highest power. 4 = 2², 6 = 2 × 3, 8 = 2³, so LCM = 2³ × 3 = 24.
When would I use the LCM in real life?
Scheduling repeating events: if one bus comes every 12 minutes and another every 18, they arrive together every lcm(12, 18) = 36 minutes.
What is the LCM of two prime numbers?
Their product, because they share no factors. lcm(7, 11) = 77.