What are LCM and GCF?
Greatest Common Factor (GCF)
Also known as the Highest Common Factor (HCF), it is the largest positive integer that divides each of the integers without a remainder.
Example: GCF(12, 18) = 6, because 6 is the largest number that goes into both.
Least Common Multiple (LCM)
The smallest positive integer that is divisible by all numbers in a given set.
Example: LCM(12, 18) = 36, because 36 is the smallest number both 12 and 18 divide into.
Methods of Calculation
There are several ways to find these values. The two most common are:
Prime Factorization
Decompose each number into its prime factors. For the GCF, take the lowest power of each common prime. For the LCM, take the highest power of all primes found across the numbers.
Euclidean Algorithm
A highly efficient method for finding the GCF of two numbers by repeatedly dividing and taking the remainder until the remainder is zero. The last non-zero remainder is the GCF.
Quick Reference Table
| Numbers | GCF | LCM |
|---|---|---|
| 6, 8 | 2 | 24 |
| 12, 15 | 3 | 60 |
| 15, 20 | 5 | 60 |
| 18, 24 | 6 | 72 |
| 10, 15, 20 | 5 | 60 |
| 12, 18, 24 | 6 | 72 |