Math
LCM Calculator
Enter two or more whole numbers to get their least common multiple.
The steps show all three classroom methods: listing multiples until they match, building a prime-factorization table and taking the highest power of each prime, and using the GCF from Euclid's algorithm. The LCM is what you need for common denominators, repeating schedules, and gear or cycle problems.
Two or more positive whole numbers separated by commas or spaces. Up to 12 numbers, each up to 1,000,000,000.
Try an example
Result
LCM
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- GCF (for comparison)
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- LCM as prime factors
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- Numbers used
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Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
Use this calculator with
Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
What the lcm calculator solves
Enter two or more whole numbers to get their least common multiple. The steps show all three classroom methods: listing multiples until they match, building a A whole number above 1 whose only factors are 1 and itself.-factorization table and taking the highest power of each prime, and using the The largest number that divides evenly into every number in a set. from Euclid's algorithm. The LCM is what you need for common The bottom number of a fraction; it says how many equal parts make one whole., repeating schedules, and gear or cycle problems.
Formula
How to use it
- Type two or more whole numbers separated by commas.
- Read the LCM, then choose the method in the steps that matches how your class solves it.
- For fractions, use the LCM of the denominators as the The smallest bottom number two fractions can share so you can add or compare them..
How to read the answer
The LCM is the smallest positive number that every input divides evenly. It is never smaller than the largest input, and it equals the product only when the numbers share no factors. The prime-factor table explains the size: each prime appears with the highest power found in any input.
Common mistakes and edge cases
- Multiplying the numbers together: lcm(12, 18) is 36, not 216.
- Mixing up LCM with GCF. GCF is the largest shared divisor (6 for 12 and 18); LCM is the smallest shared multiple (36).
- Taking the lowest power of each prime; that gives the GCF. The LCM needs the highest.
- Using lcm(a, b, c) = a × b × c ÷ gcf(a, b, c). That identity is only true for two numbers.
- Including 0: every number divides 0, so lcm with 0 is 0 and has no meaning for denominators.
Worked examples
LCM of 12, 18, 30
2² × 3² × 5 = 180.
LCM
180
LCM of 4 and 6
Listing multiples: 4, 8, 12 and 6, 12.
LCM
12
Coprime numbers 7 and 9
No shared factors, so the LCM is the product 63.
LCM
63
One number divides the other
lcm(8, 24) = 24.
LCM
24
Common denominator for 1/6, 1/8, 1/12
The LCD is 24.
LCM
24
Large numbers
lcm(123456, 789012).
LCM
8,117,355,456
Invalid input
Zero and decimals are rejected.
LCM
Error
Frequently asked questions
What is the LCM of 12 and 18?+
36. Multiples of 12 are 12, 24, 36, …; multiples of 18 are 18, 36, …. The first shared one is 36. By formula: 12 × 18 ÷ gcf(12, 18) = 216 ÷ 6 = 36.
How do I find the LCM using prime factorization?+
Factor each number, then multiply the highest power of every prime that appears. 12 = 2² × 3 and 18 = 2 × 3², so lcm = 2² × 3² = 36.
How do I find the LCM of three numbers?+
Use the prime-factor table across all three, or work pairwise: lcm(12, 18, 30) = lcm(lcm(12, 18), 30) = lcm(36, 30) = 180.
What is the difference between LCM and GCF?+
The GCF is the largest number that divides all the inputs; the LCM is the smallest number all the inputs divide. For 12 and 18 the GCF is 6 and the LCM is 36, and 6 × 36 = 12 × 18.
When do I use the LCM?+
Adding or subtracting fractions (least common denominator), finding when repeating events line up (buses every 12 and 18 minutes meet every 36 minutes), and gear or cycle problems.
Can the LCM equal one of the numbers?+
Yes, whenever that number is a multiple of all the others: lcm(8, 24) = 24.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026