Math · Number Theory
LCM
Calculator
Find the Least Common Multiple of up to 10 numbers. Uses prime factorization and GCD methods with complete step-by-step solutions, multiples table, and fraction LCD application.
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LCM
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GCD
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LCM × GCD
Enter Numbers
Enter 2–10 positive integers. Click + to add more numbers.
Quick Examples
Least Common Multiple
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LCM
GCD
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LCM×GCD
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LCM
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GCD
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LCM/GCD
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Is LCM = Product?
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🔢 Prime Factorization Breakdown
📋 Step-by-Step Solution
📊 Multiples Table — Finding First Common Multiple
🍕 LCD — Adding Fractions with These Denominators
What Is the Least Common Multiple (LCM)?
The Least Common Multiple of two or more integers is the smallest positive integer that is evenly divisible by all of them. The LCM is essential for adding and subtracting fractions (finding the Least Common Denominator), scheduling repeating events, and solving modular arithmetic problems.
LCM Calculation Methods
Method 1 — Prime Factorization:
Factor each number. Take highest power of each prime. Multiply.
LCM(12, 18): 12 = 2²×3, 18 = 2×3² → LCM = 2²×3² = 4×9 = 36
Method 2 — GCD Formula (2 numbers only):
LCM(a,b) = (a × b) / GCD(a,b)
LCM(12,18) = (12×18) / GCD(12,18) = 216/6 = 36
Method 3 — Listing Multiples:
Multiples of 12: 12, 24, 36, 48...
Multiples of 18: 18, 36, 54... → First common = 36
What is the difference between LCM and GCD?
GCD (Greatest Common Divisor) is the largest number that divides all given numbers evenly. LCM (Least Common Multiple) is the smallest number that all given numbers divide evenly. For a=12 and b=18: GCD=6 (12÷6=2, 18÷6=3), LCM=36 (36÷12=3, 36÷18=2). They are related by: LCM × GCD = a × b (for two numbers).
How is LCM used to add fractions?
To add fractions with different denominators, you need a common denominator — the smallest one is the LCD (Least Common Denominator), which equals the LCM of the denominators. For example, 1/4 + 1/6: LCM(4,6) = 12. Convert: 3/12 + 2/12 = 5/12. Without LCM you'd use 24 (4×6) as the denominator, giving 6/24 + 4/24 = 10/24 = 5/12 — same answer but harder to simplify.
What is the LCM of two prime numbers?
The LCM of two prime numbers is always their product, since primes share no common factors (GCD = 1). LCM(7, 11) = 77. LCM(2, 13) = 26. More generally, if two numbers are coprime (GCD = 1), their LCM = product. This is why LCM(a,b) = a×b when a and b share no common factors.
Can LCM be smaller than the largest number?
The LCM is always greater than or equal to the largest number in the set. If the largest number is divisible by all others, then LCM equals that largest number. For example, LCM(3, 4, 12) = 12 because 12 is already divisible by 3 and 4. In general: max(a,b,...) ≤ LCM ≤ a×b×... (product).