GCF & LCM Calculator
Find the Greatest Common Factor and Least Common Multiple
Numbers: 12, 18, 24 (3 numbers)
Greatest Common Factor (GCF)
6
Also called GCD (Greatest Common Divisor)
Least Common Multiple (LCM)
72
Smallest number divisible by all
Prime Factorization
12 =2^2 × 3
18 =2 × 3^2
24 =2^3 × 3
Verification
GCF divides all numbers evenly:
12÷6=2, 18÷6=3, 24÷6=4
LCM is divisible by all numbers:
72÷12=6, 72÷18=4, 72÷24=3
Definitions
GCF (Greatest Common Factor): The largest number that divides evenly into all given numbers. Also called GCD (Greatest Common Divisor) or HCF (Highest Common Factor).
LCM (Least Common Multiple): The smallest positive number that is a multiple of all given numbers.
Common Uses
- GCF: Simplifying fractions, finding common factors
- LCM: Adding fractions with different denominators, finding common multiples
- Both are used in number theory, cryptography, and scheduling problems
Related Tools
Fractions Calculator
Add, subtract, multiply, divide fractions
Scientific Calculator
Advanced mathematical operations
Percentage Calculator
Calculate percentages easily
Percentage Change
Calculate percent increase or decrease
Decimal to Fraction
Convert decimals to fractions
Hex to Decimal
Convert between number bases