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LCM Calculator

Enter two to ten numbers to get their least common multiple.

Find
Positive whole numbers separated by commas or spaces.
Try:

Least common multiple

lcm⁡(4, 6, 15)=60\operatorname{lcm}(4,\ 6,\ 15) = 60lcm(4, 6, 15)=60

The GCF is 1, so these numbers are coprime (they share no prime factor).

Prime factorization table

Number222333555
4200
6110
15011
GCF (smallest)000
LCM (largest)211

The cells are exponents. The GCF takes the smallest exponent in each column, the LCM the largest.

Step by step

  1. 1Prime factorization
    4, 6, 154,\ 6,\ 154, 6, 15
    ↓
    4=226=2×315=3×5\begin{aligned}4 &= 2^{2}\\6 &= 2 \times 3\\15 &= 3 \times 5\end{aligned}4615​=22=2×3=3×5​

    Write every number as a product of primes.

  2. 2GCF: smallest power of each prime
    20×30×502^{0} \times 3^{0} \times 5^{0}20×30×50
    ↓
    1=11 = 11=1

    Take only the primes that all the numbers share, each to its lowest power.

  3. 3LCM: largest power of each prime
    22×31×512^{2} \times 3^{1} \times 5^{1}22×31×51
    ↓
    22×3×5=602^{2} \times 3 \times 5 = 6022×3×5=60

    Take every prime that appears anywhere, each to its highest power.

  4. 4Euclidean algorithm for 4 and 6
    6=1×4+24=2×2+0\begin{aligned}6 &= 1 \times 4 + 2\\4 &= 2 \times 2 + 0\end{aligned}64​=1×4+2=2×2+0​
    ↓
    gcd⁡(4, 6)=2\gcd(4,\ 6) = 2gcd(4, 6)=2

    Divide the larger by the smaller, then repeat with the divisor and the remainder. The last non-zero remainder is the GCF.

  5. 5Euclidean algorithm for 2 and 15
    15=7×2+12=2×1+0\begin{aligned}15 &= 7 \times 2 + 1\\2 &= 2 \times 1 + 0\end{aligned}152​=7×2+1=2×1+0​
    ↓
    gcd⁡(2, 15)=1\gcd(2,\ 15) = 1gcd(2, 15)=1

    Divide the larger by the smaller, then repeat with the divisor and the remainder. The last non-zero remainder is the GCF.

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About LCM Calculator

This LCM calculator finds the least common multiple of up to ten whole numbers, the smallest number that every one of them divides into, and shows how. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.

The page opens on 4, 6 and 15. Their prime factorizations are 2², 2 × 3 and 3 × 5, and taking the largest power of every prime gives 2^2 × 3 × 5 = 60. A second method is listing multiples until the first match: for 6 and 8 that is 24.

The LCM is what you use as the common denominator when adding fractions and to find when repeating events line up, such as two buses that leave every 4 and 6 minutes.

How to use LCM Calculator

  1. 1Choose LCM and GCF, LCM only or GCF only.
  2. 2Type two to ten positive whole numbers separated by commas or spaces.
  3. 3Read the answer at the top. It updates as you type.
  4. 4Check the prime exponent table: the GCF uses the smallest exponents and the LCM the largest.
  5. 5Open the steps for the Euclidean algorithm and, for two numbers, the link lcm = a × b ÷ gcd.

Features

  • LCM and GCF (GCD, HCF) of 2 to 10 numbers at once.
  • Prime factorization method with an exponent table.
  • Euclidean algorithm shown division by division.
  • Coprime detection.
  • Numbers of up to 24 digits, computed exactly with big integers.
  • Separate LCM-only and GCF-only views.
  • Step list in KaTeX with a copy button for the LaTeX.

LCM

Take every prime that appears in any number, each to its largest power.

lcm(4, 6, 15) = 2² × 3 × 5 = 60
lcm(a, b) = a × b / gcd(a, b)

Worked examples

  • LCM of 4, 6 and 15 → gives 60

    2² × 3 × 5 = 60.

  • LCM of 6 and 8 → gives 24

    Multiples of 6: 6, 12, 18, 24. Multiples of 8: 8, 16, 24. The first match is 24.

Privacy: how it works

  • Everything is calculated by code running in your browser tab. The numbers you enter are not sent to Ulkaa or to any other server, and there is nothing to sign in to.

Tips

  • To add fractions, use the LCM of the denominators as the common denominator, which keeps the numbers small.
  • To simplify a fraction, divide top and bottom by their GCF in one step.
  • If the GCF of two numbers is 1, their LCM is just their product.

Frequently asked questions

Is it really free?

Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.

Do I need an account?

No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.

Does it run in my browser?

Yes. Numbers are processed by code running in your browser tab, on your own device.

Is my data uploaded?

No. Numbers are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.

How do I find the LCM of two numbers?

Factor each into primes and multiply every prime to its highest power, or divide the product of the numbers by their GCF.

What is the LCM of two coprime numbers?

Their product. The LCM of 8 and 15 is 120, because they share no prime factor.

More LCM and GCF Calculator pages

  • LCM and GCF CalculatorEnter two to ten whole numbers to get their least common multiple and greatest common factor, with the working.
  • GCF CalculatorEnter two to ten numbers to get their greatest common factor.
  • GCD CalculatorEnter numbers to get the greatest common divisor, with every Euclidean step.
  • HCF CalculatorEnter numbers to get their highest common factor, with the working.

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