The greatest common factor finds the largest shared divisor. The least common multiple finds the smallest positive number shared by two or more multiples. They solve different kinds of problems.
Greatest common factor
The GCF of 18 and 24 is 6 because 6 is the largest number that divides both. Use it to simplify fractions or divide items into the largest equal groups.
Least common multiple
The LCM of 4 and 6 is 12 because 12 is the first positive multiple shared by both. Use it to align repeating schedules or find a common denominator.
Prime-factor method
Write 18 = 2 × 3² and 24 = 2³ × 3. The GCF uses the lower powers, 2 × 3 = 6. The LCM uses the higher powers, 2³ × 3² = 72.
Check the context
Grouping questions usually point to GCF; synchronization questions usually point to LCM. Verify the answer by dividing or listing early multiples rather than relying only on a label.
Sources
The figures and rules in this guide are checked against:
- Greatest Common Divisor — Wolfram MathWorld
- Least Common Multiple — Wolfram MathWorld
- Fundamental Theorem of Arithmetic — Wolfram MathWorld
- Greatest common factor — Khan Academy