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GCF & LCM Calculator.

Calculate Greatest Common Factor (GCF) and Least Common Multiple (LCM) of numbers

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Results update as you type.

Calculation Type

Common Examples:

GCF Examples:
GCF(12, 18) = 6
GCF(24, 36) = 12
GCF(15, 25) = 5
LCM Examples:
LCM(12, 18) = 36
LCM(4, 6) = 12
LCM(3, 5) = 15

What is GCF and LCM?

Greatest Common Factor (GCF)

The GCF, also known as the Greatest Common Divisor (GCD), is the largest positive integer that divides both numbers without leaving a remainder. For example, the GCF of 12 and 18 is 6, because 6 is the largest number that divides both 12 and 18 evenly.

Least Common Multiple (LCM)

The LCM is the smallest positive integer that is divisible by both numbers. For example, the LCM of 4 and 6 is 12, because 12 is the smallest number that both 4 and 6 divide into evenly.

How to Calculate GCF

  1. List all factors of both numbers
  2. Find the common factors
  3. Select the greatest common factor

How to Calculate LCM

  1. List the multiples of both numbers
  2. Find the common multiples
  3. Select the least common multiple

Relationship Between GCF and LCM

For any two numbers a and b, the relationship is: a × b = GCF(a, b) × LCM(a, b). This means that if you know the GCF and one of the values, you can calculate the LCM.

Common Uses

  • GCF: Simplifying fractions, dividing items into equal groups, finding common denominators
  • LCM: Finding common denominators, solving word problems about repeating events, scheduling

FAQs

What is GCF?

GCF (Greatest Common Factor) is the largest positive integer that divides each of the numbers without remainder.

What is LCM?

LCM (Least Common Multiple) is the smallest positive integer that is divisible by each of the numbers.

How to Use the GCF & LCM Calculator

Find the Greatest Common Factor and Least Common Multiple of two or more numbers.

  1. Enter two or more whole numbers.
  2. See the GCF and LCM with their relationship.

GCF & LCM Formulas

GCF (Euclid)

gcd(a, b) = gcd(b, a mod b)

Repeat until the remainder is 0.

Example:

Input: gcd(12, 18)

Calculation: gcd(18,12)→gcd(12,6)→gcd(6,0)

Result: 6

LCM

lcm(a, b) = a × b / gcd(a, b)

Product divided by the GCF.

Example:

Input: 12, 18

Calculation: 12 × 18 / 6

Result: 36

Real-World Use Cases

Fractions

Use the LCM to find a common denominator.

Scheduling

LCM finds when repeating events align.

Tips

Tips

  • GCF × LCM = product of the two numbers.
  • The GCF is never larger than the smallest input.