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LCM Calculator

Your Results

The least common multiple of 12, 18 and 30 is 180, the smallest number all of them divide into evenly (180 ÷ 12 = 15, 180 ÷ 18 = 10, 180 ÷ 30 = 6). In prime factors it's 2² × 3² × 5, and every other common multiple, such as 360, is a multiple of it.

180
LCM of 12, 18, 30
2² × 3² × 5
LCM in Prime Factors
15, 10, 6
LCM ÷ Each Number
360, 540
Next Common Multiples
6,480
All Numbers Multiplied

Need the largest number that divides them all instead? Open the GCF Calculator with these numbers.

NumberPrime FactorsAs Powers
122 × 2 × 322 × 3
182 × 3 × 32 × 32
302 × 3 × 52 × 3 × 5
LCM18022 × 32 × 5

Take every prime that appears, at the highest power it has in any one number, and multiply them.

What Is the Least Common Multiple?

The least common multiple (LCM), also called the lowest common multiple, is the smallest whole number that two or more numbers all divide into evenly. For 6 and 10 it's 30: it's in the 6 times table and the 10 times table, and no smaller number is in both.

  • Adding fractions: the LCM of the denominators is the least common denominator. To add 1/6 and 1/10, rewrite both over 30.
  • Things that repeat: if one bus comes every 12 minutes and another every 18, they arrive together every 36 minutes, the LCM.

Which calculator should I use?

  • LCM Calculator: the smallest number all of your numbers divide into, as when finding a common denominator to add fractions.
  • GCF Calculator: the opposite, the largest number that divides all of your numbers (also called the GCD or HCF), as when simplifying a fraction.

How to Calculate the LCM

For two numbers, divide their product by their greatest common factor:

LCM(a,b)= a×bGCF(a,b)
  • a and b: the two numbers.
  • GCF(a, b): their greatest common factor. Find it by dividing the bigger number by the smaller and repeating with the remainder until it's 0 (Euclid's method); the last number you divided by is the GCF. The GCF Calculator shows these steps.

For three or more numbers, find the LCM of the first two, then the LCM of that answer and the next number, and so on. Other ways to find it:

  • Prime factorization: break each number into primes and multiply every prime at the highest power it has in any one number.
  • Ladder (cake) method: divide the row of numbers by a prime that goes into at least two of them, carry the others down, and repeat. Multiply the primes down the side by the numbers left at the bottom.
  • Listing multiples: write out each number's multiples until a number appears on every list. Easy for small numbers, slow for big ones.

Example

The LCM of 12, 18, 30:

  • 12 = 2 × 2 × 3
  • 18 = 2 × 3 × 3
  • 30 = 2 × 3 × 5
  • Highest powers: 2 appears twice (in 12), 3 appears twice (in 18), 5 appears once (in 30), so the LCM = 2 × 2 × 3 × 3 × 5 = 180.
  • Check by listing: 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180; 18: 18, 36, 54, 72, 90, 108, 126, 144, 162, 180; 30: 30, 60, 90, 120, 150, 180. 180 is the first number on all three lists.

How to Use the LCM Calculator

"What's the least common multiple of 12, 18 and 30, and how do I show the work?" This calculator answers that.

Let's enter the numbers for this example in the box. They are already filled in when the calculator opens, so you can follow along and then change them to your own.

  • Numbers: Enter 12, 18, 30. Use from 2 to 10 whole numbers, each from 1 up to just under 1 billion, separated by commas or spaces. Don't put commas inside a number: type 2500, not 2,500.

Calculate and Reset

Click Calculate to see your results. If the box has a problem, such as a decimal, a 0, a single number or more than 10, a message pops up under it instead. With the default numbers you get:

  • Your Results: the LCM (180) with each number divided into it, and the LCM in prime factors.
  • LCM: the headline number, 180.
  • LCM in Prime Factors: 2² × 3² × 5.
  • LCM ÷ Each Number: 15, 10, 6, how many of each number fit into the LCM.
  • Next Common Multiples: 360 and 540. Every common multiple is a multiple of the LCM.
  • All Numbers Multiplied: 6,480, which is always a common multiple too, but usually not the least.
  • GCF Calculator link: opens the GCF Calculator with the same numbers filled in.
  • Primes, Ladder, Multiples and GCF Method: four tables that show the working each way, so you can follow the method your class uses.
  • Share Results: a link that opens this calculator with your numbers filled in. Copy it, or share it on Facebook or X.

Click Reset to put the box back to 12, 18, 30 and show the default results again. Very large answers are shown in full, however many digits they have.