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Mixed Number Calculator

Reference

LCM Calculator

Find the least common multiple of two, three, four, or five numbers at once. Type each number and watch the prime factorization and the result update instantly — no button required.

Live — updates as you type

Numbers

View step-by-step working

    Method

    The Prime Factorization Method

    Worked Example — LCM of 12 and 18

    Break each number into primes, then take the highest power of every prime that appears in either list.

    1. Factor each number

      12 = 2 × 2 × 3  ·  18 = 2 × 3 × 3

    2. List every prime that appears

      2 and 3

    3. Take the highest power of each

      2² (from 12) and 3² (from 18)

    4. Multiply

      4 × 9 = 36

    LCM(12, 18) = 36

    12 2 × 2 × 3 2 2 3 18 2 × 3 × 3 2 3 3 Take every prime factor at its highest power from either list LCM = 36

    More Examples

    LCM Across Different Number Sets

    Two small numbers

    LCM(4, 6) = 12

    One divides the other

    LCM(3, 9) = 9

    When one number divides the other, the LCM is just the larger number.

    No shared factors

    LCM(5, 7) = 35

    Coprime numbers — their LCM is simply their product.

    Three numbers

    LCM(2, 3, 4) = 12

    Larger numbers

    LCM(15, 20) = 60

    Four numbers

    LCM(2, 3, 5, 6) = 30

    Why It Matters

    Where the LCM Actually Gets Used

    Inside fraction arithmetic, the least common multiple of two denominators is exactly what gets called the least common denominator, or LCD, once it's being used to add or subtract fractions rather than compared as bare numbers. The math is identical either way — the LCM calculator here and the dedicated LCD calculator will always agree on the same two numbers.

    Outside fractions, the LCM shows up anywhere repeating cycles need to synchronize. Two gears with 12 and 18 teeth return to their starting alignment every 36 rotations of the smaller gear's reference tooth — the LCM of their tooth counts. A bus that runs every 15 minutes and one that runs every 20 minutes leave the depot together again every 60 minutes.

    The prime-factorization method scales cleanly to any number of inputs, which is why it's the standard approach taught in school and the one this calculator uses under the hood — list the factors, take the highest power of every prime, multiply. The multiply-and-divide-by-GCF shortcut is faster for exactly two numbers but doesn't extend directly to three or more without applying it repeatedly.

    Whichever method you reach for, the result is always at least as large as the biggest number in the set, since a common multiple by definition has to be divisible by every one of them.

    Common Mistakes

    Where LCM Calculations Go Wrong

    Quick Reference

    LCM Values for Common Number Pairs

    Search or scroll this table for the least common multiple of frequently paired numbers — useful for checking homework or double-checking a mental calculation.

    Least common multiple reference table for common number pairs
    NumbersLCM
    2, 3 6
    2, 4 4
    2, 5 10
    3, 4 12
    3, 5 15
    3, 6 6
    4, 5 20
    4, 6 12
    4, 8 8
    5, 6 30
    5, 8 40
    5, 10 10
    6, 8 24
    6, 9 18
    6, 10 30
    7, 8 56
    7, 9 63
    7, 14 14
    8, 9 72
    8, 10 40
    8, 12 24
    9, 10 90
    9, 12 36
    10, 12 60
    10, 15 30
    12, 15 60
    12, 16 48
    12, 18 36
    15, 20 60
    16, 20 80

    Alternative Method

    Finding the LCM by Listing Multiples

    Before reaching for prime factorization, many people first learn a slower but more visual method: write out the multiples of each number until one appears in both lists.

    1. List multiples of the first number

      4, 8, 12, 16, 20

    2. List multiples of the second number

      6, 12, 18, 24, 30

    3. Find the first value that appears in both

      12

    LCM(4, 6) = 12

    This method is easy to understand and works fine for small numbers, but it becomes slow and error-prone once the numbers grow or a third and fourth number join the problem — which is exactly where the prime-factorization method above earns its keep.

    Questions

    Frequently Asked Questions

    Questions specific to the least common multiple, not already covered elsewhere on the site.

    What is the least common multiple?

    The least common multiple (LCM) of two or more numbers is the smallest number that every one of them divides into evenly. The LCM of 4 and 6 is 12, since 12 is the smallest number both 4 and 6 divide into with no remainder.

    How is the LCM different from the GCF?

    The greatest common factor (GCF) is the largest number that divides evenly INTO both numbers, while the LCM is the smallest number both numbers divide evenly INTO. For 8 and 12, the GCF is 4 and the LCM is 24 — they move in opposite directions.

    Is the LCM ever smaller than either original number?

    No. The LCM is always at least as large as the larger of the two numbers, since it has to be a multiple of both.