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LCM Calculator with steps

Enter two or more whole numbers to get their least common multiple, worked out from the prime factorization of each one.

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Answer

Enter your numbers or pick an example — the answer and the steps appear here instantly.

What the LCM calculator shows

  • Each number in primes

    12 = 2² × 3, 18 = 2 × 3², 30 = 2 × 3 × 5: every input is broken into prime powers first.

  • The highest powers

    For every prime that appears anywhere, the largest exponent is kept, here 2², 3² and 5.

  • The product

    Multiplying those powers gives the LCM, in this case 4 × 9 × 5 = 180.

How to find an LCM with the calculator

  1. List your numbers

    Type positive whole numbers separated by commas, for example 8, 12, 20. You can enter up to 500 of them, each as large as 10¹².

  2. Calculate

    The factorization of each number, the LCM and a numbered outline appear immediately. The LCM is an exact whole number however large it gets, so it never needs the ≈ mark that flags rounded values.

  3. Use the result

    Copy the LCM. If you want the reasoning in prose, the “Explain step by step” button asks the AI Math Solver for it; treat that text as a second opinion that may slip, and trust the outline when the two disagree. All of the calculating happens in your browser, free.

Three ways to find the LCM by hand

  • List the multiples

    Good for small numbers. Multiples of 4: 4, 8, 12, 16. Multiples of 6: 6, 12, 18. The first number in both lists, 12, is the LCM.

  • Use prime factorization

    Factor each number, take every prime at its highest power and multiply. For 12, 18 and 30: 2² × 3² × 5 = 180. Check: 180 ÷ 12 = 15, 180 ÷ 18 = 10, 180 ÷ 30 = 6.

  • Use the GCF for two numbers

    LCM(a, b) = a × b ÷ GCF(a, b). For 12 and 18, GCF = 6, giving an LCM of 216 ÷ 6 = 36. This shortcut does not carry over directly to three numbers.

  • Where you need it

    The LCM of the denominators is the least common denominator. To add 1/12 + 5/18, rewrite both over 36: 3/36 + 10/36 = 13/36.

Frequently asked questions

The LCM is the smallest number that all of your numbers divide into; the GCF is the largest number that divides all of them. For 12 and 18, the LCM is 36 and the GCF is 6.

You can enter up to 500 positive whole numbers, each no bigger than 10¹² (one trillion). Zero, negatives and decimals are not accepted, because the LCM here is defined for positive integers.

Yes. Primes share no factors, so the LCM of 7 and 11 is 77. The same holds for any two numbers whose GCF is 1, such as 8 and 9, whose LCM is 72.

Listing multiples gets slow when the numbers are large or share few factors. Prime factorization reaches the answer directly and shows why it is the least common multiple.

Not for the calculator, which is free, runs in your browser and asks for no account. Credits apply only to the AI explanation: 2 per explanation without a plan, or covered by the Pro plans* (*fair use: up to 300 runs a day combined over the writing, study and code tools). If you are not signed in, the first part is still visible as a free preview.

Use it to confirm answers and to practice the method. If your class restricts calculators or AI tools on homework or tests, follow that rule.

Number theory and fraction tools

Find the LCM in one step

Type your numbers and see the prime factorizations that lead to the least common multiple.

Find LCM
  • Two or more numbers
  • Highest prime powers shown
  • Exact, even for big numbers