Arithmetic
LCM Calculator
Find the least common multiple of two or more whole numbers — the smallest number they all divide into evenly. Enter your numbers and watch the answer, prime factorization, and step-by-step working update live.
Enter your numbers
3 validn1
n2
n3
Least common multiple
24
LCM(4, 6, 8) = 24
= 2³ × 3
GCF of the set
2
Count
3
Prime factorization check
4 = 2²
6 = 2 × 3
8 = 2³
LCM = 2^3 × 3
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The basics
What is the least common multiple?
The least common multiple of a set of whole numbers is the smallest positive number every one of them divides into without a remainder. It is the meeting point of their times tables — the first multiple they all share. There are two ways to look at it, and they always agree.
multiples of 4: 4, 8, 12, 16…
It is a shared multiple
List the multiples of each number and look for the first value that appears in every list. That shared value is the LCM — never smaller than the largest number you started with.
LCM(4, 6) = 12
LCM(a, b) = (a × b) ÷ GCF(a, b)
It pairs with the GCF
The LCM and the greatest common factor are two sides of one coin. For any two numbers a and b, their LCM times their GCF equals their product — so knowing one gives you the other.
(4 × 6) ÷ 2 = 12
Method
How to find the LCM by hand
The GCF method is the fastest for two numbers and scales cleanly to a whole list.
- 1
Find the GCF of the first two numbers
Use the greatest common factor of a and b — the largest number that divides both. The Euclidean algorithm or a quick factor list both work.
GCF(4, 6) = 2 - 2
Divide the product by the GCF
Multiply the two numbers, then divide by their GCF. That single division gives the LCM of the pair.
(4 × 6) ÷ 2 = 12 - 3
Fold in the next number
For three or more, take the LCM you just found and combine it with the next number the same way. With a third number of 8, fold it into the 12 from step 2. Repeat until the list runs out.
LCM(12, 8) = 24
Worked examples
Three methods, one answer
Every textbook teaches the LCM three ways. Here is the same problem — LCM(12, 18) — solved by each. Switch tabs to see them line up.
Find LCM(12, 18)
Factor each: 12 = 2² × 3, 18 = 2 × 3²
Take the highest power of every prime that appears:
2^2 × 3^2
Multiply them together.
LCM(12, 18) = 36
Same answer, three routes. 2 × 2 × 3 × 3 = 36.
Where it shows up
Why the LCM matters
A small idea that quietly powers fraction arithmetic, schedules, and anything that repeats on a cycle.
LCD = LCM of denominators
Adding fractions
To add fractions with different denominators, you rewrite them over a common one. The smallest choice — the least common denominator — is exactly the LCM of the denominators. If you want the fractions rewritten too, use the LCD calculator.
buses every 12 & 18 min
Scheduling
When two repeating events start together, the LCM of their intervals tells you the next time they coincide. Buses, traffic lights, shift rotations — all LCM problems.
teeth that line up again
Gears & cycles
Two meshing gears return to their starting alignment after a number of turns set by the LCM of their tooth counts. The same logic governs planetary alignments and signal cycles.
Quick chart
What is the LCM of X and Y?
Pick a first number and read its LCM with every common partner at a glance — the fast answer to “LCM of 4 and 6”, “LCM of 6 and 8”, and the rest.
LCM ofand the numbers below
LCM(4, 2)
LCM(4, 3) · coprime
LCM(4, 4) · equal
LCM(4, 5) · coprime
LCM(4, 6)
LCM(4, 7) · coprime
LCM(4, 8)
LCM(4, 9) · coprime
LCM(4, 10)
LCM(4, 11) · coprime
LCM(4, 12)
LCM(4, 13) · coprime
When two numbers share no common factor (coprime), their LCM is simply their product.
Worth knowing
Rules worth remembering
A handful of facts make LCM problems quicker and let you sanity-check any answer.
LCM(a, b) × GCF(a, b) = a × b
The LCM–GCF identity
For two numbers, the LCM times the GCF always equals their product. It is the quickest way to find one when you know the other.
LCM(a, b) ≥ max(a, b)
Never smaller than the largest
The LCM is at least as big as the biggest number in the set, because it has to be a multiple of it. If your answer is smaller, something went wrong.
coprime ⇒ LCM = a × b
Coprime numbers
When two numbers share no common factor, their GCF is 1, so their LCM is just their product. No shortcut needed beyond multiplying.
a | b ⇒ LCM = b
Multiples collapse
If one number divides the other, the larger one is already the LCM. There is nothing to build up to.
LCM(a, a) = a
A number with itself
The LCM of any number with itself is just that number — its first shared multiple is itself.
order doesn't matter
Commutative & associative
You can take the numbers in any order and group them however you like. The fold across a list always lands on the same result.
Watch out
Common mistakes
Most wrong LCM answers come from a few predictable slips. Catch them before they cost you.
LCM ≠ GCF
Confusing LCM with GCF
The GCF goes down (the biggest shared factor); the LCM goes up (the smallest shared multiple). If your answer for two distinct numbers came out smaller than both, you found the GCF by mistake.
not always a × b
Always multiplying
Multiplying the numbers only gives the LCM when they are coprime. When they share a factor, the product overshoots — you must divide by the GCF.
take the highest power
Lowest vs highest power
In the prime-factorization method the LCM takes the highest power of each prime, not the lowest. Taking the lowest power gives the GCF instead.
stop at the first match
Listing too far
When listing multiples, stop at the very first value that appears in both lists. Any later shared multiple is a multiple of the LCM, not the LCM itself.
Compare
LCM vs GCF, side by side
They are computed from the same prime factors but pull in opposite directions. Using 12 and 18 as the example:
GCF
LCM
Question it answers
Largest shared factor
Smallest shared multiple
Prime powers used
Lowest of each prime
Highest of each prime
Size
≤ smallest number
≥ largest number
For 12 and 18
6
36
Coprime numbers
1
their product
FAQ
Common questions
The least common multiple of two or more whole numbers is the smallest positive number that each of them divides into evenly. For example, the LCM of 4 and 6 is 12 — the smallest number that is a multiple of both 4 and 6.
For two numbers a and b, divide their product by their greatest common factor: LCM = (a × b) ÷ GCF. For 4 and 6 the GCF is 2, so LCM = (4 × 6) ÷ 2 = 12. For more than two numbers, take the LCM of the first two, then the LCM of that result with the next number, and so on.
There are three standard methods. Prime factorization: factor each number and take the highest power of every prime. The GCF method: divide the product of the numbers by their greatest common factor. Listing multiples: list the multiples of each number and find the first one they share. All three give the same answer.
The LCM is most commonly used to add or subtract fractions with different denominators: the LCM of the denominators is the least common denominator (LCD), the smallest shared denominator you can rewrite each fraction over. It also appears in scheduling problems, like finding when repeating events line up again, and in working with gears and cycles.
The greatest common factor (GCF) is the largest number that divides into all the values, so it is never larger than the smallest value. The least common multiple (LCM) is the smallest number that all the values divide into, so it is never smaller than the largest value. GCF goes down, LCM goes up — and for two numbers, LCM × GCF = the product of the numbers.
If two numbers share no common factor other than 1 (they are coprime), their GCF is 1, so their LCM is simply their product. The LCM of 8 and 9 is 72, and the LCM of 4 and 15 is 60.
Yes. When one number is a multiple of the other, the larger number is the LCM. The LCM of 3 and 12 is 12, because 12 is already a multiple of 3. The LCM is never smaller than the largest number in the set.
Fold the operation across the list: find the LCM of the first two numbers, then find the LCM of that result with the third number, and continue. For 3, 4, and 6: LCM(3, 4) = 12, then LCM(12, 6) = 12. Prime factorization also works directly — take the highest power of every prime across all the numbers at once.
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Ugo CharlesBuilt and fact-checked against our editorial standards · Last updated June 2026
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