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About This Calculator
The least common multiple is the smallest number that two or more integers divide into evenly, essential for adding fractions with different denominators. This calculator finds the LCM using prime factorization or the relationship between LCM and GCF, handling multiple numbers simultaneously. Scheduling problems frequently rely on LCM — for example, determining when two cyclical events with different periods will next coincide.
Quick Tips
- 1 LCM is the smallest number that both values divide into evenly.
- 2 LCM x GCF of two numbers always equals the product of those two numbers.
- 3 Use prime factorization — take the highest power of each prime factor.
Example Calculation
Two machines cycle every 18 and 24 minutes — when do they sync?
LCM(18, 24) = 72 minutes | Both align every 1 hour 12 minutes
What Is the Least Common Multiple?
The LCM is the smallest positive number that is a multiple of two or more numbers. For example, LCM(12, 18) = 36, because 36 is the smallest number divisible by both 12 and 18. The LCM is essential for adding fractions with different denominators.
How to Find the LCM
Method 1: List multiples until you find a common one. Method 2: Use prime factorization — take the highest power of each prime factor. Method 3: Use the formula LCM(a,b) = |a×b| / GCF(a,b). This calculator shows the steps using prime factorization.
LCM Using Prime Factorization
Factor each number into primes. For each prime, take the highest power that appears. LCM(12,18): 12 = 2² × 3, 18 = 2 × 3². Take 2² and 3², so LCM = 4 × 9 = 36. This method works for any number of inputs.
LCM in Everyday Applications
LCM is used to find common denominators when adding fractions, schedule recurring events (two buses running on different schedules), synchronize cycles, and solve timing problems. It answers: "When will these two patterns coincide again?"
Frequently Asked Questions
For any two numbers a and b: LCM(a,b) × GCF(a,b) = a × b. This means if you know one, you can calculate the other. For example, LCM(12,18) × GCF(12,18) = 36 × 6 = 216 = 12 × 18.
Yes. If one number is a multiple of the other, the LCM is the larger number. For example, LCM(4, 12) = 12, because 12 is already a multiple of 4.
The LCM of two different prime numbers is always their product. For example, LCM(7, 11) = 77. Prime numbers have no common factors other than 1.
Yes. Find the LCM of the first two, then find the LCM of that result with the third number, and so on. This calculator supports up to three numbers.