Common Multiple Calculator
Find common multiples and LCM of multiple numbers with step-by-step explanations
Calculate Common Multiples
Least Common Multiple (LCM)
First 10 Common Multiples
Pattern: All common multiples are multiples of the LCM (6)
Example Calculations
Example 1: Numbers 4 and 6
Multiples of 4: 4, 8, 12, 16, 20, 24...
Multiples of 6: 6, 12, 18, 24, 30...
LCM = 12
Common multiples: 12, 24, 36, 48...
Example 2: Numbers 8, 12, 18
Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72...
Multiples of 12: 12, 24, 36, 48, 60, 72...
Multiples of 18: 18, 36, 54, 72...
LCM = 72
Mathematical Notation
Properties
LCM is always ≥ largest input number
All common multiples are multiples of LCM
LCM × GCD = product of two numbers
Common multiples form an infinite sequence
Understanding Common Multiples
What are Common Multiples?
A common multiple is a number that is a multiple of two or more given numbers. For example, 12 is a common multiple of 3 and 4 because 12 = 3 × 4 and 12 = 4 × 3.
Least Common Multiple (LCM)
The LCM is the smallest positive common multiple. It's useful in:
- •Adding/subtracting fractions
- •Solving time-based problems
- •Pattern recognition
- •Number theory applications
Calculation Methods
1. Prime Factorization Method
Find prime factors of each number, then take the highest power of each prime.
2. Division Method
Divide all numbers by their common factors until no common factors remain.
3. Formula Method
LCM(a,b) = |a × b| ÷ GCD(a,b)