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Least Common Multiple Calculator

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Results

Least common multiple is 30.

Least common multiple
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How to use this calculator

  1. Enter First positive integer value
    Enter the first positive integer in this field. 1
  2. Enter Second positive integer value
    Enter the second positive integer in this field. 1
  3. Read Least common multiple

Least common multiple () vs First positive integer value ()

66666701011000000

Least common multiple () First positive integer value ()

What this calculates

Imagine the multiples of each input as separate lists. A common multiple appears in both lists. Their overlap gives you a concrete picture of the calculation. 2

Cuemath describes LCM for two or more numbers. Its equation uses a and b. The excerpt pairs a broad description with a two-symbol formula. 2

Using the calculator

Enter a positive integer in each field. The page uses the pair together in one calculation. It returns the LCM as a computed result. 1

Formula used

The page computes lcm_value = first_value * second_value / gcd(first_value, second_value). 1

Calculation stages

Product: multiply the two entered values. Shared factor: find the divisor used by the formula. Quotient: divide the product by that factor to obtain the result. 1

Worked examples

Source formula example — LCM of 6 and 10: Least common multiple 30

See inputs and calculation

Starting values

First positive integer value
6
Second positive integer value
10
    1. Least common multiple: 30
      Show arithmetic
      6 * 10 / gcd(6, 10)

    Source formula example — LCM of 12 and 21: Least common multiple 84

    See inputs and calculation

    Starting values

    First positive integer value
    12
    Second positive integer value
    21
      1. Least common multiple: 84
        Show arithmetic
        12 * 21 / gcd(12, 21)
      Original example and source context

      Answer: 6, 10 → 30. CalculatorSoup's example says LCM(6,10) = 30. Its origin is CalculatorSoup's published calculator. 1

      Inputs: use 6 and 10 as the pair. Shared-factor stage: CalculatorSoup gives GCF(6,10) = 2. Product-and-division stage: its excerpt shows (6×10)/2 = 60/2 = 30. 1

      A prime-factor method

      CalculatorSoup gives a prime-factor route. Find all the prime factors of each given number. Keep each prime as often as it occurs most for any one given number. Then multiply the retained list to find the LCM. 1

      Formula terms

      Here, first_value and second_value are the entered values. gcd(first_value, second_value) names their greatest common factor, or GCF. CalculatorSoup defines GCF as the largest number shared by all the factors. lcm_value names the least common multiple returned by the formula. 1

      Key facts

      • Cuemath writes HCF as the divisor in its displayed equation. 2
      • Cuemath's displayed equation uses a and b. 2
      • CalculatorSoup frames its formula for two integers, a and b. 1

      How this is calculated

      For each input, enter a positive integer from 1 through 1,000,000. These are this page's input limits, not limits of the LCM formula. The page derives the greatest common factor from the two inputs and applies LCM(a,b) = (a × b) / GCF(a,b) to return their least common multiple.

      Least common multiple

      product ÷ gcd(first_value, second_value)
      • product = Product
      • first_value = First positive integer value ()
      • second_value = Second positive integer value ()
      • gcd = the greatest common divisor of two positive integers
      Understand each part

      These names are shorthand for the exact calculations below, not different formulas.

      1. Product (product)

        Multiply the two input values.

        See the definition of productfirst_value * second_value
      Follow the calculation with your values
      1. Least common multiple: 30
        Show arithmetic
        6 * 10 / gcd(6, 10)
      Full formulas, symbols and sources

      lcm_value = first_value * second_value / gcd(first_value, second_value)

      first_value
      First positive integer value ()
      second_value
      Second positive integer value ()
      lcm_value
      Least common multiple
      gcd
      the greatest common divisor of two positive integers

        Frequently asked questions

        Does Cuemath spell out HCF?
        Cuemath uses HCF as the divisor in its formula. The excerpt does not expand that abbreviation. 2
        Does the formula explain why it divides by the shared factor?
        CalculatorSoup states the product-and-GCF relationship as a rule. The excerpt gives no separate derivation. 1
        Do the published example values include units?
        The CalculatorSoup excerpt gives its example without naming units. Read the quoted row as the published values and result. 1
        Does the calculator use prime factors internally?
        CalculatorSoup gives prime-factor instructions for finding an LCM. The excerpt does not say which method the calculator uses internally. 1
        Does CalculatorSoup define “evenly divisible”?
        The excerpt uses that phrase in its LCM definition. It does not explain the phrase separately. 1
        What does the excerpt say a prime factor is?
        The excerpt tells you to find prime factors but does not define the term. 1

        Limitations & common mistakes

        • The page accepts each input only from 1 to 1000000 and refuses outside that range.
        • That range is the page's choice, not a limit of the formula.
        • Results are computed from inputs, only as exact as those inputs, and cannot replace measurement or professional judgement where required.

        By Editorial Team, Assembled from the cited primary sources; not yet expert-reviewed

        Last updated

        Sources current as of

        How we review

        Formula, sources, and review

        This calculation follows the formula published on this page and rests on 2 cited sources, listed under Sources below. Last checked .

        How we review

        Sources & methodology

        Sources

        • 1 LCM Calculator - Least Common Multiple — last verified
        • 2 LCM (Least Common Multiple) | Lowest Common Multiple | How to Find LCM? — last verified