Common Multiple Calculator

Find common multiples and LCM of multiple numbers with step-by-step explanations

Calculate Common Multiples

#1
#2

Least Common Multiple (LCM)

6
LCM(2, 3) = 6

First 10 Common Multiples

6
6 × 1
12
6 × 2
18
6 × 3
24
6 × 4
30
6 × 5
36
6 × 6
42
6 × 7
48
6 × 8
54
6 × 9
60
6 × 10

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

LCMLeast Common Multiple
GCDGreatest Common Divisor
Natural Numbers
×Multiplication
÷Division

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)