Reference
LCM Calculator
Find the least common multiple of two, three, four, or five numbers at once. Type each number and watch the prime factorization and the result update instantly — no button required.
Numbers
View step-by-step working
Method
The Prime Factorization Method
Worked Example — LCM of 12 and 18
Break each number into primes, then take the highest power of every prime that appears in either list.
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Factor each number
12 = 2 × 2 × 3 · 18 = 2 × 3 × 3
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List every prime that appears
2 and 3
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Take the highest power of each
2² (from 12) and 3² (from 18)
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Multiply
4 × 9 = 36
LCM(12, 18) = 36
More Examples
LCM Across Different Number Sets
Two small numbers
LCM(4, 6) = 12
One divides the other
LCM(3, 9) = 9
When one number divides the other, the LCM is just the larger number.
No shared factors
LCM(5, 7) = 35
Coprime numbers — their LCM is simply their product.
Three numbers
LCM(2, 3, 4) = 12
Larger numbers
LCM(15, 20) = 60
Four numbers
LCM(2, 3, 5, 6) = 30
Why It Matters
Where the LCM Actually Gets Used
Inside fraction arithmetic, the least common multiple of two denominators is exactly what gets called the least common denominator, or LCD, once it's being used to add or subtract fractions rather than compared as bare numbers. The math is identical either way — the LCM calculator here and the dedicated LCD calculator will always agree on the same two numbers.
Outside fractions, the LCM shows up anywhere repeating cycles need to synchronize. Two gears with 12 and 18 teeth return to their starting alignment every 36 rotations of the smaller gear's reference tooth — the LCM of their tooth counts. A bus that runs every 15 minutes and one that runs every 20 minutes leave the depot together again every 60 minutes.
The prime-factorization method scales cleanly to any number of inputs, which is why it's the standard approach taught in school and the one this calculator uses under the hood — list the factors, take the highest power of every prime, multiply. The multiply-and-divide-by-GCF shortcut is faster for exactly two numbers but doesn't extend directly to three or more without applying it repeatedly.
Whichever method you reach for, the result is always at least as large as the biggest number in the set, since a common multiple by definition has to be divisible by every one of them.
Common Mistakes
Where LCM Calculations Go Wrong
Quick Reference
LCM Values for Common Number Pairs
Search or scroll this table for the least common multiple of frequently paired numbers — useful for checking homework or double-checking a mental calculation.
Alternative Method
Finding the LCM by Listing Multiples
Before reaching for prime factorization, many people first learn a slower but more visual method: write out the multiples of each number until one appears in both lists.
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List multiples of the first number
4, 8, 12, 16, 20
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List multiples of the second number
6, 12, 18, 24, 30
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Find the first value that appears in both
12
LCM(4, 6) = 12
This method is easy to understand and works fine for small numbers, but it becomes slow and error-prone once the numbers grow or a third and fourth number join the problem — which is exactly where the prime-factorization method above earns its keep.
Questions
Frequently Asked Questions
Questions specific to the least common multiple, not already covered elsewhere on the site.