Common Multiples Calculator
Enter 2–15 positive integers and choose how many shared multiples to list. The first result is the LCM.
First positive common multiples of
LCM fold steps
Each LCM becomes the first value in the next pair.
Private by design: calculations stay in this browser tab. Your integers and list count are not added to the URL, history, storage, cookies, requests, or analytics.
What is a common multiple?
A positive common multiple of a group of integers is a positive whole number divisible by every integer in that group. For 3, 4, and 6, the sequence starts 12, 24, 36, 48, and 60. Each term divides evenly by all three inputs.
There is no final positive common multiple. Once the least common multiple is known, multiplying it by each positive integer produces the full sequence. This page therefore lists the exact number of terms you request instead of claiming to list them all.
The first common multiple is the LCM
The least common multiple (LCM) is the smallest positive integer divisible by every entered value. It is the first term in the common-multiples sequence. For 3, 4, and 6, the LCM is 12, so the next terms are 12 × 2, 12 × 3, 12 × 4, and so on.
This relationship keeps the result auditable: the page shows one LCM, the exact first-N sequence generated from it, and no separate mode with a competing answer.
Worked example: 3, 4, and 6
The first fold calculates LCM(3, 4). Because GCF(3, 4) = 1, the formula gives 3 ÷ 1 × 4 = 12. The next fold calculates LCM(12, 6). Because GCF(12, 6) = 6, the formula gives 12 ÷ 6 × 6 = 12.
With a requested count of 10, the calculator multiplies 12 by 1 through 10 and returns 12, 24, 36, 48, 60, 72, 84, 96, 108, and 120.
How more than two integers are folded
The calculator moves from left to right. It finds the LCM of the first pair, then combines that result with the next integer. Each visible step uses LCM(a, b) = a ÷ GCF(a, b) × b. Dividing before multiplying preserves exact integer arithmetic and keeps intermediate values smaller.
Repeated inputs are allowed because they do not change the set of shared multiples. The page keeps them in the normalized input receipt so the calculation remains traceable to what you entered.
Input limits and exactness
Enter 2–15 base-10 positive whole integers separated by spaces, commas, or new lines. Each integer may contain at most 15 digits. Choose a list count from 1 to 100. Zero, negative values, decimals, fractions, plus signs, exponent notation, and other symbols are rejected.
The engine uses JavaScript BigInt division, remainder, multiplication, and addition. Entered integers and calculated multiples are never converted to floating point, so the displayed whole-number results are not rounded.
What this calculator does not do
This page does not draw a number line, solve word problems, factor polynomials, accept fractional inputs, or calculate an unbounded list. GCF is used only inside the LCM method; use the related GCF calculator when the greatest common factor itself is your primary result.
Frequently asked questions
What are the first ten common multiples of 3, 4, and 6?
They are 12, 24, 36, 48, 60, 72, 84, 96, 108, and 120. Every value in that list is divisible by 3, 4, and 6.
Is the first positive common multiple the LCM?
Yes. The least common multiple, or LCM, is the smallest positive common multiple. Every later positive common multiple is the LCM multiplied by 2, 3, 4, and so on.
How does the calculator find common multiples?
It folds through the entered integers to find their exact LCM. Each fold uses LCM(a, b) = a ÷ GCF(a, b) × b. It then multiplies the final LCM by 1 through the requested list count.
How many common multiples can I list?
Choose any whole-number count from 1 to 100. The result states the requested count and never claims to list every common multiple, because positive common multiples continue without end.
Can I enter zero, negative numbers, decimals, or fractions?
No. This calculator accepts 2–15 strictly positive whole integers. Zero, negative values, decimals, fractions, plus signs, and scientific notation are rejected.