LCM Calculator
Find the least common multiple (LCM) of two or more numbers
LCM Methods
What is the Least Common Multiple?
The least common multiple (LCM) is the smallest positive integer that is divisible by two or more numbers. For example, the LCM of 4 and 6 is 12 because 12 is the smallest number that both 4 and 6 divide into evenly.
LCM is essential for adding fractions with different denominators, scheduling recurring events, and solving problems involving cycles. When you find a common denominator for 1/4 + 1/6, you're finding the LCM of 4 and 6.
LCM and GCF are inversely related: for any two numbers a and b, LCM(a,b) × GCF(a,b) = a × b. This relationship provides an efficient way to calculate LCM once you know the GCF.
Methods to Find LCM
Listing Multiples
List multiples of each number until you find the first common one.
Prime Factorization
Use highest power of each prime factor present in any number.
Using GCF
LCM = (a × b) / GCF(a,b). Fast when GCF is known.
Division Method
Divide numbers by common primes, multiply all divisors.
Common LCM Examples
Reference table for frequently needed LCM calculations:
| Numbers | LCM | GCF | Product |
|---|---|---|---|
| 2, 3 | 6 | 1 | 6 |
| 4, 6 | 12 | 2 | 24 |
| 3, 5 | 15 | 1 | 15 |
| 6, 8 | 24 | 2 | 48 |
| 12, 15 | 60 | 3 | 180 |
| 4, 6, 8 | 24 | 2 | N/A |
Real-World Applications
Adding Fractions
Find LCM of denominators to get common denominator. For 1/4 + 1/6: LCM(4,6)=12, so 3/12 + 2/12 = 5/12.
Scheduling
Events repeating every 4 and 6 days coincide every LCM(4,6)=12 days. Useful for maintenance schedules.
Gear Cycles
Gears with 12 and 18 teeth align every LCM(12,18)=36 tooth movements. Important in machinery.
Timing Signals
Flashing lights at 3 and 5 second intervals both flash together every LCM(3,5)=15 seconds.
Frequently Asked Questions
Is LCM always larger than the numbers?
LCM is always at least as large as the largest number. If one number divides the other, LCM equals the larger number. Otherwise, LCM is larger than both.
What's the LCM if numbers share no common factors?
For coprime numbers (GCF=1), LCM equals the product. LCM(3,7) = 21 because 3 and 7 share no factors except 1.
How do I find LCM of fractions?
LCM of fractions = LCM of numerators / GCF of denominators. For 2/3 and 4/5: LCM = LCM(2,4)/GCF(3,5) = 4/1 = 4.
Can I find LCM of more than two numbers?
Yes! Find LCM of first two, then LCM of that result with the third, and so on. LCM(4,6,8) = LCM(LCM(4,6),8) = LCM(12,8) = 24.
Pro Tips
- Bookmark this calculator for quick access in the future
- Use the share button to send your results to others
- Try different scenarios to compare outcomes
- Check out our related calculators for more insights
Found this calculator helpful? Share it with others: