LCM & GCD
LCM and GCD (HCF)
These two concepts are fundamental to arithmetic, especially when working with fractions.
Definitions
LCM (Least Common Multiple):
The smallest positive number that is a multiple of two or more numbers.
Usage: Finding a common denominator for adding fractions.
The smallest positive number that is a multiple of two or more numbers.
Usage: Finding a common denominator for adding fractions.
GCD (Greatest Common Divisor):
Also called HCF (Highest Common Factor). The largest number that divides two or more numbers without a remainder.
Usage: Simplifying fractions to their lowest terms.
Also called HCF (Highest Common Factor). The largest number that divides two or more numbers without a remainder.
Usage: Simplifying fractions to their lowest terms.
Example: 12 and 18
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 18: 1, 2, 3, 6, 9, 18
- GCD: 6
- Multiples of 12: 12, 24, 36...
- Multiples of 18: 18, 36...
- LCM: 36
The Relation
For any two numbers a and b:
LCM(a, b) × GCD(a, b) = a × b