LCM Calculator - Least Common Multiple

LCM calculator at a glance#

The least common multiple (LCM) of two numbers is the smallest positive whole number that both numbers divide into evenly. An LCM calculator finds it for you: enter two or more numbers and it returns the smallest value that is a multiple of every one of them.

You can find the LCM two ways by hand. List the multiples of each number until one matches: the multiples of 4 are 4, 8, 12, 16, and the multiples of 6 are 6, 12, 18, so the first shared multiple, and the LCM of 4 and 6, is 12. Prime factorization gives the same answer: 4 is 2 times 2, and 6 is 2 times 3, so you take the highest power of each prime, 2 squared times 3, which is 4 times 3, or 12.

Enter your numbers in the calculator above for the exact LCM, and pick a method to see the prime factorization or listing steps worked out. The LCM is always at least as large as the bigger number, and when two numbers share no common factor it is simply their product.

Ways to find the LCM by hand#

Beyond listing multiples and prime factorization, a few methods give the same answer and suit different number sizes.

GCF shortcut (two numbers)#

For exactly two numbers, find their greatest common factor (GCF) first, then use LCM(a, b) = (a times b) divided by GCF(a, b). For 6 and 8 the GCF is 2, so the LCM is (6 times 8) divided by 2 = 48 divided by 2 = 24. This is the fastest route once you know the GCF.

Division (ladder) method#

Write the numbers in a row and divide the whole row by a prime that goes into at least one of them, carrying down anything it does not divide. Repeat until the bottom row is all 1s. Multiply every divisor you used: that product is the LCM. It scales cleanly to three or more numbers, unlike the GCF shortcut.

Worked example: scheduling#

One team trains every 4 days and another every 6 days, both starting today. They next train together on the LCM of 4 and 6. The multiples of 4 are 4, 8, 12 and the multiples of 6 are 6, 12, so they line up at day 12. That is the everyday use of the LCM: the point where two repeating cycles next coincide.

LCM FAQ#

How do you find the LCM using prime factorization?#

Break each number into primes, then for every prime that appears take its highest power and multiply those together. For 8 (2 cubed) and 12 (2 squared times 3), take 2 cubed and 3, giving 8 times 3 = 24. So LCM(8, 12) = 24.

Can an LCM calculator handle more than two numbers?#

Yes. Enter all the numbers and the calculator returns the smallest value every one divides into. The division and prime-factorization methods both extend to three or more numbers, while the GCF shortcut works only for pairs.

What is the division (ladder) method?#

Divide the row of numbers by shared prime factors until only 1s remain, then multiply all the divisors. For 15 and 20, divide by 5 to get 3 and 4, then by 3 and by 2 (each affecting one number), so the LCM is 5 times 3 times 4 = 60.

What is the difference between a common multiple and the least common multiple?#

A common multiple is any number that all the inputs divide into; there are infinitely many. The least common multiple is the smallest of them. For 20 and 30, common multiples include 60, 120 and 180, but the least is 60.

Why are prime factors useful for finding the LCM?#

The LCM must include enough of each prime to cover every input. Taking the highest power of each prime that appears guarantees the result is divisible by all of them and no larger than necessary, which is exactly the smallest common multiple.

Is the LCM ever just the product of the two numbers?#

Yes, when the numbers share no common factor (their GCF is 1). For 4 and 5 there is no shared factor, so the LCM is 4 times 5 = 20. When they do share factors, the LCM is smaller than the product.