Least Common Factor Calculator

Find the smallest common prime factor and least common multiple of numbers

Calculate Least Common Factor & Multiple

Enter Numbers (2-15 numbers)

Calculation Method

Prime Factorization

Most comprehensive method

GCD Formula

Using LCM = (a×b)/GCD

List Multiples

Visual approach

Show step-by-step solution

Calculation Results

Enter at least 2 valid numbers (≥ 2) to calculate LCF and LCM

Example Calculation

Find LCF and LCM of 12 and 18

Given numbers: 12 and 18

Goal: Find the smallest common prime factor and LCM

Prime Factorization Method

1. Prime factorizations:

• 12 = 2² × 3

• 18 = 2 × 3²

2. Common prime factors: 2, 3

3. Least Common Factor (LCF) = 2

4. LCM = 2² × 3² = 4 × 9 = 36

Results: LCF = 2, LCM = 36

Key Concepts

LCF

Least Common Factor

Smallest non-trivial prime factor shared by all numbers

LCM

Least Common Multiple

Smallest positive integer divisible by all numbers

Coprime Numbers

Numbers with no common prime factors (GCD = 1)

Quick Reference

LCM Formula

LCM(a,b) = (a × b) / GCD(a,b)

Common Examples

LCM(4, 6) = 12

LCM(8, 12) = 24

LCM(15, 25) = 75

LCM(7, 11) = 77 (coprime)

Applications

• Fraction operations
• Gear ratios
• Event scheduling
• Number theory

Understanding Least Common Factor vs. Least Common Multiple

Least Common Factor (LCF)

The Least Common Factor is the smallest non-trivial prime number that divides all numbers in a set. It helps identify whether numbers are coprime (relatively prime) - numbers that share no common prime factors except 1.

How to Find LCF:

1.Find prime factorization of each number
2.Identify common prime factors
3.Select the smallest common prime factor
4.If no common factors exist, numbers are coprime

Least Common Multiple (LCM)

The Least Common Multiple is the smallest positive integer that is divisible by all numbers in a set. It's essential for adding fractions, solving periodic problems, and finding common denominators.