LCM & GCF Calculator

Calculate the Least Common Multiple (LCM) and Greatest Common Factor (GCF) of two or more numbers with step-by-step solutions.

LCM & GCF Calculator

Enter 2 to 6 numbers to calculate their Least Common Multiple and Greatest Common Factor.

Number of Values:

Number 1

Number 2

Least Common Multiple (LCM)

Greatest Common Factor (GCF)

Number: 12

Prime Factorization:

2^2 × 3

2²

Number: 18

Prime Factorization:

2 × 3^2

3²

Show step-by-step solution

Step-by-Step Solution

Step 1: Prime Factorization

12 = 2^2 × 3

18 = 2 × 3^2

Step 2: Calculate LCM

LCM is found by multiplying the highest power of all primes that appear in any of the numbers.

Step 3: Calculate GCF

GCF is found by multiplying the lowest power of all common primes across all numbers.

Step 4: Results

LCM(12, 18) = 36
GCF(12, 18) = 6

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Calculation History

1 saved calculations

Numbers: 12, 18

LCM: 36, GCF: 6

9/26/2025, 1:51:55 AM

Understanding LCM and GCF

What is LCM (Least Common Multiple)?

The Least Common Multiple (LCM) of two or more numbers is the smallest positive integer that is divisible by each of the numbers without a remainder. It's useful for finding a common denominator when adding or subtracting fractions, scheduling recurring events, and solving various mathematical problems.

What is GCF (Greatest Common Factor)?

The Greatest Common Factor (GCF), also known as the Greatest Common Divisor (GCD), is the largest positive integer that divides each of the numbers without a remainder. It's useful for simplifying fractions, factoring polynomials, and solving various mathematical problems.

Calculation Methods

Prime Factorization Method

Find the prime factors of each number. For LCM, multiply the highest power of all primes. For GCF, multiply the lowest power of common primes.

Euclidean Algorithm

An efficient method for finding the GCF of two numbers. Based on the principle that GCF(a, b) = GCF(b, a mod b). The LCM can then be found using LCM(a, b) = (a × b) / GCF(a, b).

Real-World Applications

Fraction operations - LCM for common denominators, GCF for simplifying fractions
Scheduling - Finding when events will coincide (LCM of time intervals)
Engineering - Gear ratios, circuit design, and pattern recognition
Computer science - Cryptography, algorithm optimization, and data structures
Music theory - Rhythm patterns and harmonic intervals
Architecture - Proportional design and measurement standardization

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