Least Common Multiple (LCM) Calculator
LCM Calculator
How to Find the Least Common Multiple
The Least Common Multiple (LCM) of two or more positive integers is the smallest positive integer divisible by each of them.
Method 1: GCF Identity (used above)
- Find the GCF (Greatest Common Factor) using the Euclidean algorithm.
- Apply the identity: LCM = (a × b) / GCF.
Method 2: Prime Factorization
- Find the prime factorization of each number.
- For each prime that appears in any factorization, take the highest exponent across all inputs.
- Multiply these prime powers together.
Example: LCM(12, 18) via prime factorization
- 12 = 2² × 3¹
- 18 = 2¹ × 3²
- Take the highest exponent of each prime: 2² (from 12), 3² (from 18).
- LCM = 2² × 3² = 4 × 9 = 36
Method 3: Listing Multiples
- List the multiples of each number until you find a common one.
- That smallest common multiple is the LCM.
This is the slowest method for large inputs; the GCF identity is preferred.
Popular LCM Examples
Frequently Asked Questions
What is the Least Common Multiple (LCM)?
The LCM is the smallest positive integer that is a multiple of two or more given numbers. It is widely used to find common denominators of fractions and to solve scheduling problems.
How are LCM and GCF related?
By the identity LCM(a, b) × GCF(a, b) = a × b. So once you have the GCF (via the Euclidean algorithm), the LCM follows immediately: LCM = (a × b) / GCF.
What is LCM used for?
Two major uses: (1) adding/subtracting fractions with different denominators (find the common denominator); (2) scheduling — when two repeating events occur together (every 12 days and every 18 days → coincide every LCM(12, 18) = 36 days).
Related Calculators
- Greatest Common Factor (GCF) Calculator
- Prime Factorization Calculator
- Divisors of a Number
- Multiples of a Number
- Fraction Calculator (uses LCM for common denominators)
LCM Calculator
