How this instrument works
The least common multiple of three numbers extends the familiar two-number case the same way its GCD counterpart does: find the LCM of the first pair, then take the LCM of THAT result with the third number. Because any multiple shared by all three numbers must, in particular, be a multiple of the first two, combining them first loses nothing.
This site's other LCM-related pages cover exactly two numbers; this page extends that identical machinery to a third, useful for genuinely three-way scheduling questions — three events recurring every so many days, three gears with different tooth counts, or three medications each due on their own separate cycle, all needing to know when every cycle lines back up together at once.
Order doesn't matter here either: lcm(lcm(a,b),c) always gives the identical result as combining the three numbers in any other order — the least common multiple of three numbers is a single, well-defined value.
- Enter the first number into the First number field.
- Enter the second and third numbers into their own fields.
- Read Least common multiple: the smallest number all three divide into evenly.
- Divide that result by each of the three original numbers and confirm every division comes out whole.
Worked example — three events every 4, 6, and 10 days
Three events recurring every 4, 6, and 10 days: lcm(4,6)=12 first, and then lcm(12,10)=60 — so all three events next coincide again in exactly 60 days. Checking: 60÷4=15, 60÷6=10, and 60÷10=6, every division landing on a whole number.
3, 5, and 7 share no common factors at all, so their combined LCM is simply their product, 3×5×7=105. Three identical numbers, 2, 2, and 2, have a combined LCM of just 2 itself — nothing new to reach beyond the shared value.
Questions
How do you find the LCM of three numbers?
Find the LCM of any two of them first, then find the LCM of that result with the remaining third number — the answer comes out identical regardless of which pair is combined first.
What does the LCM of three recurring cycles represent?
The soonest point at which all three cycles line back up together simultaneously — a scheduling question that shows up whenever multiple recurring events, each on their own separate period, need to be tracked at once.
How is this different from this site's plain LCM calculator?
That page covers exactly two numbers; this page extends the identical shared-multiple idea to a third number, for genuinely three-way scheduling and cycle questions.
What if the three numbers share no common factors at all?
Then their LCM is simply their straight product — with nothing shared between them, the smallest number divisible by all three is just multiplying them together directly.
Can this be extended to four or more numbers?
Yes — the identical pairwise-combining approach extends to any number of values, folding one more number in at a time; this page is scoped to three specifically to keep the calculation concrete.