GCF & LCM Calculator | Find Greatest Common Factor and Least Common Multiple
Use the GCF & LCM Calculator to quickly find the greatest common factor and least common multiple of any numbers.
GCF & LCM Calculator
Find Greatest Common Factor and Least Common Multiple with detailed steps
Greatest Common Factor (GCF)
Find the largest number that divides all given numbers
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Least Common Multiple (LCM)
Find the smallest number that is a multiple of all given numbers
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Find Both GCF and LCM
Calculate both values at once with detailed comparisons
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Find All Factors
List all factors of given numbers and identify common factors
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📖 How to Use This Calculator
- GCF (Greatest Common Factor): The largest number that divides all given numbers evenly
- LCM (Least Common Multiple): The smallest number that all given numbers divide into evenly
- Multiple Methods: Choose from different calculation methods to see various approaches
- Add Numbers: Calculate GCF/LCM for 2 or more numbers (up to 10)
- Step-by-Step: See detailed explanations of each calculation step
- Visual Aids: Prime factorization trees and factor highlighting
- Quick Examples: Try pre-loaded examples to understand the concepts
What is a common factor?
A common factor of two or more numbers is any number that divides evenly into all of them. For example, the common factors of 12 and 18 are 1, 2, 3, and 6.
Can the GCF of two numbers be greater than either number?
No. The Greatest Common Factor (GCF) of two numbers can never be greater than the smallest of the two numbers. It will always be less than or equal to the smallest number.
What is the GCF of 12 and 18?
The factors of 12 are {1, 2, 3, 4, 6, 12}. The factors of 18 are {1, 2, 3, 6, 9, 18}. The greatest common factor is 6.
What is the GCF of 24 and 36?
The factors of 24 are {1, 2, 3, 4, 6, 8, 12, 24}. The factors of 36 are {1, 2, 3, 4, 6, 9, 12, 18, 36}. The greatest common factor is 12.
What is the GCF of 8 and 12?
The factors of 8 are {1, 2, 4, 8}. The factors of 12 are {1, 2, 3, 4, 6, 12}. The greatest common factor is 4.
What is the GCF of 6 and 8?
The factors of 6 are {1, 2, 3, 6}. The factors of 8 are {1, 2, 4, 8}. The greatest common factor is 2.
What is the GCF of 6 and 9?
The factors of 6 are {1, 2, 3, 6}. The factors of 9 are {1, 3, 9}. The greatest common factor is 3.
What is the GCF of 12 and 16?
The factors of 12 are {1, 2, 3, 4, 6, 12}. The factors of 16 are {1, 2, 4, 8, 16}. The greatest common factor is 4.
What is the GCF of 12 and 20?
The factors of 12 are {1, 2, 3, 4, 6, 12}. The factors of 20 are {1, 2, 4, 5, 10, 20}. The greatest common factor is 4.
What is the GCF of 4 and 6?
The factors of 4 are {1, 2, 4}. The factors of 6 are {1, 2, 3, 6}. The greatest common factor is 2.
What is the GCF of 10 and 8?
The factors of 10 are {1, 2, 5, 10}. The factors of 8 are {1, 2, 4, 8}. The greatest common factor is 2.
What is the GCF of 15 and 20?
The factors of 15 are {1, 3, 5, 15}. The factors of 20 are {1, 2, 4, 5, 10, 20}. The greatest common factor is 5.
What is the GCF of 16 and 24?
The factors of 16 are {1, 2, 4, 8, 16}. The factors of 24 are {1, 2, 3, 4, 6, 8, 12, 24}. The greatest common factor is 8.
What is the GCF of 24 and 32?
The factors of 24 are {1, 2, 3, 4, 6, 8, 12, 24}. The factors of 32 are {1, 2, 4, 8, 16, 32}. The greatest common factor is 8.
What is the Least Common Factor?
The term "Least Common Factor" is not a standard mathematical concept in the same way GCF or LCM are. If it refers to the smallest common divisor, then for any set of positive integers, the least common factor is always 1.
What is the Least Common Multiple (LCM)?
The Least Common Multiple (LCM) of two or more non-zero whole numbers is the smallest positive integer that is a multiple of all the numbers.
How to find the Least Common Multiple (LCM)?
There are several methods:
- **Listing Multiples:** List the multiples of each number until you find the first common multiple.
- **Prime Factorization:** Find the prime factorization of each number. For each prime factor, take the highest power that appears in any of the factorizations and multiply them together.
- **Using GCF:** For two numbers 'a' and 'b', LCM(a, b) = (a × b) / GCF(a, b).
What is a common multiple?
A common multiple of two or more numbers is any number that is a multiple of all of them. For example, common multiples of 6 and 8 include 24, 48, 72, etc.
What is the LCM of 8 and 12?
Multiples of 8: {8, 16, 24, 32, ...}. Multiples of 12: {12, 24, 36, ...}. The least common multiple is 24.
What is the LCM of 6 and 8?
Multiples of 6: {6, 12, 18, 24, ...}. Multiples of 8: {8, 16, 24, 32, ...}. The least common multiple is 24.
What is the LCM of 6 and 9?
Multiples of 6: {6, 12, 18, 24, ...}. Multiples of 9: {9, 18, 27, ...}. The least common multiple is 18.
What is the LCM of 9 and 12?
Multiples of 9: {9, 18, 27, 36, ...}. Multiples of 12: {12, 24, 36, ...}. The least common multiple is 36.
What is the LCM of 4 and 10?
Multiples of 4: {4, 8, 12, 16, 20, ...}. Multiples of 10: {10, 20, 30, ...}. The least common multiple is 20.
What is the LCM of 4 and 6?
Multiples of 4: {4, 8, 12, ...}. Multiples of 6: {6, 12, 18, ...}. The least common multiple is 12.
What is the LCM of 3 and 4?
Multiples of 3: {3, 6, 9, 12, ...}. Multiples of 4: {4, 8, 12, ...}. The least common multiple is 12.
What is the LCM of 10 and 12?
Multiples of 10: {10, 20, 30, 40, 50, 60, ...}. Multiples of 12: {12, 24, 36, 48, 60, ...}. The least common multiple is 60.
What is the LCM of 3 and 5?
Since 3 and 5 are prime numbers, their LCM is their product: 3 × 5 = 15.
Is 0 ever used when finding GCF or LCM?
For GCF, GCF(a, 0) = |a|. However, LCM involving 0 is typically undefined because 0 has infinitely many multiples (0, 0, 0, ...), and there is no smallest non-zero common multiple.
Which method is fastest for large numbers?
For finding the GCF of large numbers, the Euclidean Algorithm is generally the most efficient. For LCM, once the GCF is found, the relationship LCM(a, b) = (a × b) / GCF(a, b) provides a fast way to calculate it.