Quick answer
Common multiples of a and b are the multiples of their least common multiple. For 4 and 6 the LCM is 12 and the first five common multiples are 12, 24, 36, 48 and 60.
Enter two positive integers. The calculator returns the first five common multiples and the LCM.
Related tools: Common Factor Calculator: All common factors of two numbers. Slope Calculator: Slope, angle, distance and line equation through two points. LCM Calculator: Least common multiple of two or more numbers.
How to use the Common Multiple Calculator
- Enter first number (a whole number, between 1 and 1000000).
- Enter second number (a whole number, between 1 and 1000000).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| First number | A whole number | ≥ 1, ≤ 1000000 |
| Second number | A whole number | ≥ 1, ≤ 1000000 |
Formula and method
Formula
common multiples = k × lcm(a, b)
IEEE-754 double precision; shown to at most 6 decimal places.
Every common multiple is a multiple of the LCM.
Worked examples
This example is verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: First number = 4; Second number = 6.
| Result | Value |
|---|---|
| First five common multiples | 12, 24, 36, 48, 60 |
| LCM | 12 |
The first line is the headline result (first five common multiples). Below it the common Multiple Calculator lists lCM, which describe the same case from other angles. IEEE-754 double precision; shown to at most 6 decimal places.
Finding the LCM
LCM(a, b) = a × b ÷ gcd(a, b) = 24 ÷ 2 = 12. Every common multiple is k × 12.
Applications
Use common multiples to add fractions with different denominators (denominators 4 and 6 use 12) or to find when two cycles line up: buses every 4 and 6 minutes meet every 12 minutes.
How the result changes with first number
Holding every other input at the first worked example, this table changes only first number. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| First number | First five common multiples | LCM |
|---|---|---|
| 2 | 6, 12, 18, 24, 30 | 6 |
| 4 | 12, 24, 36, 48, 60 | 12 |
| 8 | 24, 48, 72, 96, 120 | 24 |
| 16 | 48, 96, 144, 192, 240 | 48 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Second number: entering "0" shows "Second number must be at least 1." beside that field and no result.
Choosing between the Common Multiple Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Common Factor Calculator](/math/common-factor-calculator/) | first number and second number | Common factors |
| [Slope Calculator](/math/slope-calculator/) | x₁, y₁ and x₂ | Slope |
| [LCM Calculator](/math/lcm-calculator/) | numbers | Least common multiple |
| [Factor Calculator](/math/factor-calculator/) | number | Factors |
| [Quadratic Formula Calculator](/math/quadratic-formula-calculator/) | a, b and c | Roots |
Background: algebra
Many algebra calculators rest on the same ideas: write the problem in a standard form, identify the coefficients, apply the formula and check the answer by substituting it back. For a quadratic ax² + bx + c = 0 the roots are (−b ± √(b² − 4ac)) ÷ 2a, and the discriminant b² − 4ac decides the kind of roots: positive gives two real roots, zero gives one repeated root and negative gives two complex conjugate roots.
If a = 0 the equation is linear, not quadratic. A sign slip on the −b term shifts both roots by the same amount, so substitute your roots back to check.
Assumptions and limitations
- Positive integers
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for second number to confirm this.
Frequently asked questions
What is the LCM of 3 and 5?
The LCM of 3 and 5 is 15, since they share no factor.
Are there infinitely many common multiples?
Yes. Every multiple of the LCM is a common multiple, so the list never ends.
What is the difference between LCM and GCF?
LCM is the smallest common multiple, GCF the largest common divisor.
What does the Common Multiple Calculator calculate?
First common multiples of two numbers. It returns First five common multiples and LCM.
What formula does the Common Multiple Calculator use?
common multiples = k × lcm(a, b). Every common multiple is a multiple of the LCM.
What do I need to enter in the common Multiple Calculator?
You enter First number and Second number.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Positive integers.
What is an example of a common Multiple result?
With first number 4 and second number 6, the first five common multiples is 12, 24, 36, 48, 60.
Related calculators
- Common Factor Calculator — All common factors of two numbers.
- Slope Calculator — Slope, angle, distance and line equation through two points.
- LCM Calculator — Least common multiple of two or more numbers.
- Factor Calculator — List every factor of a positive whole number.
- Quadratic Formula Calculator — Solve ax² + bx + c = 0, including complex roots.
- Log Calculator — Logarithm of a number to any base.
- Antilog Calculator — Inverse logarithm: raise a base to a power.
- Average Rate of Change Calculator — Average rate of change between two points.
- System of Equations Calculator — Solve two linear equations in two unknowns.
Sources
- OpenStax, Algebra and Trigonometry 2e (Rice University): exponents, radicals, logarithms and inverse trigonometric functions
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.