About

The Greatest Common Factor (GCF) and Least Common Multiple (LCM) are fundamental concepts in arithmetic, essential for simplifying fractions and solving scheduling problems. The GCF is the largest integer that divides all numbers in a set without leaving a remainder. The LCM is the smallest integer that is a multiple of all numbers in the set.

Students often struggle to see the connection between the raw numbers and the result. This tool solves that by generating a Prime Factorization Tree for every input. By breaking numbers down into their atomic prime components (e.g., 12 = 2 × 2 × 3), the shared factors become visually obvious.

Formulas

The relationship between GCF and LCM for two numbers a and b is:

LCM(a, b) = |a × b|GCF(a, b)

GCF is typically found using the Euclidean Algorithm:

GCF(a, 0) = a
GCF(a, b) = GCF(b, a mod b)

Reference Data

Numbers (a, b)	GCF (a,b)	LCM (a,b)
8, 12	4	24
9, 15	3	45
12, 18	6	36
24, 36	12	72
18, 30	6	90
25, 30	5	150
20, 50	10	100
42, 56	14	168

Frequently Asked Questions

There is no difference. GCF (Greatest Common Factor) and GCD (Greatest Common Divisor) are synonymous terms used in different regions or textbooks to describe the same concept.

Yes. This tool supports up to 6 different numbers simultaneously. The GCF of a set is the number that divides all of them.

Prime numbers have no common factors other than 1. Therefore, the only way to find a common multiple is to multiply them together (e.g., LCM of 3 and 5 is 3 × 5 = 15).