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What is LCM (Least Common Multiple)?
The Least Common Multiple (LCM) of two numbers is the smallest positive number that is divisible by both numbers.
For example, LCM(4, 6) = 12, because 12 is the smallest number divisible by both 4 and 6.
LCM is calculated using the formula: LCM(a, b) = |a × b| / GCD(a, b), where GCD is the Greatest Common Divisor.
How to Find LCM
There are several methods to find LCM:
- Prime factorization: Find prime factors of each number, take the highest power of each prime
- Using GCD: LCM(a,b) = |a×b| / GCD(a,b)
- Listing multiples: List multiples of each number until you find the first common one
This calculator uses the GCD method for speed and accuracy.
LCM Applications
LCM is used to find common denominators when adding fractions, synchronize recurring events (scheduling), and solve problems involving repeating cycles.
For example, if Bus A comes every 12 minutes and Bus B every 18 minutes, they'll arrive together every LCM(12,18) = 36 minutes.
Часто задаваемые вопросы
What is LCM of 12 and 18?
LCM(12, 18) = 36. Both 12 and 18 divide evenly into 36.
What's the difference between LCM and GCF?
LCM (Least Common Multiple) is the smallest shared multiple. GCF (Greatest Common Factor) is the largest shared factor. For example, LCM(4,6)=12 and GCF(4,6)=2.
Can LCM be one of the numbers?
Yes, if one number is a multiple of the other. For example, LCM(3, 9) = 9.