The least common multiple (LCM) is the smallest positive integer that is a multiple of each number in a given set. It helps with fraction denominators, repeating schedules, and number theory problems. An LCM calculator can quickly check the result.
How to use an LCM calculator
- Open the Least Common Multiple Calculator.
- Enter the positive integers you want to compare.
- Run the calculation.
- Review the LCM and verify that it is divisible by every input number.
Method 1: list the multiples
To find the LCM of 4 and 6, list multiples of 4: 4, 8, 12, 16, 20, 24. Multiples of 6: 6, 12, 18, 24. The smallest common positive multiple is 12.
Method 2: prime factorization
Write each number as a product of primes and keep the highest power of every prime that appears. For example, 12 = 2² × 3 and 18 = 2 × 3². The LCM is 2² × 3² = 36.
Method 3: use the greatest common divisor
For positive integers a and b, LCM(a,b) = (a × b) ÷ GCD(a,b). For 12 and 18, the greatest common divisor is 6. Therefore, LCM = (12 × 18) ÷ 6 = 36.
LCM examples
| Numbers | LCM | Reason |
|---|---|---|
| 3 and 5 | 15 | They are coprime |
| 6 and 8 | 24 | 24 is divisible by both |
| 9 and 12 | 36 | 36 is the first common positive multiple |
| 4, 6 and 10 | 60 | 60 is divisible by all three |
Using LCM to add fractions
When adding 1/6 and 1/8, find LCM(6,8) = 24. Then 1/6 = 4/24 and 1/8 = 3/24, so 1/6 + 1/8 = 7/24. The LCM gives the least common denominator.
Using LCM for repeating events
Suppose one event repeats every 6 days and another every 8 days, and both occur today. They next occur together after 24 days, assuming the schedules continue without changes.
LCM vs GCD
The LCM is the smallest positive shared multiple; the GCD is the largest positive integer that divides all the inputs. They answer different questions, even though the two are mathematically related.
Frequently asked questions
What is the LCM of 8 and 12?
24.
What is the LCM of two coprime numbers?
Their product. For example, LCM(7, 9) = 63.
Can the LCM be smaller than the largest input?
For positive integers, no. The LCM must be at least as large as the largest input.
Is LCM useful for more than two numbers?
Yes. Find the LCM of the first pair, then find the LCM of that result and the next number.
Check your answers using the Least Common Multiple Calculator.
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