LCM Calculator

Find the least common multiple of two or more numbers, with three worked methods.

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Least common multiple

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The least common multiple of a set of numbers is the smallest positive number that every one of them divides into exactly. For example, the LCM of 12 and 18 is 36. This calculator handles two to five numbers and shows the full working for all three standard methods. For the largest shared divisor instead, use the GCF calculator.

LCM vs "least common factor"

A quick clarification, because these two get mixed up constantly. The least common multiple is a real and useful idea — the smallest number that all your inputs divide into.

The phrase "least common factor" is not useful, because the answer is always 1. Every whole number is divisible by 1, so 1 is the smallest factor any set of numbers can share. If you searched for that term, you almost certainly want either the LCM (this page) or the greatest common factor.

Method 1 — Listing multiples

The most direct method: write out multiples of each number until you find one they share.

Worked example — LCM of 4 and 6:

Multiples of 4: 4, 8, 12, 16, 20, 24, …
Multiples of 6: 6, 12, 18, 24, 30, …
Shared multiples: 12, 24, …

The smallest shared multiple is 12, so LCM(4, 6) = 12.

This method is clear for small numbers, but it becomes impractical fast — for 48 and 60 you would need to list 20 multiples before finding 240.

Method 2 — Prime factorization

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

Worked example — LCM of 12 and 18:

12 = 2² × 3
18 = 2 × 3²
Highest power of 2: 2² (from 12)
Highest power of 3: 3² (from 18)

LCM = 2² × 3² = 4 × 9 = 36.

Notice the contrast with the GCF, where you take the lowest power of shared primes instead. Use the prime factorization calculator to factorize any number.

Method 3 — The GCF formula

For two numbers, this is the fastest approach:

LCM(a, b) = (a × b) ÷ GCF(a, b)

Worked example — LCM of 48 and 60:

GCF(48, 60) = 12
48 × 60 = 2880
2880 ÷ 12 = 240

So LCM(48, 60) = 240. Compare that to listing 20 multiples of 48 by hand.

This formula works only for pairs. For three or more numbers, apply it step by step: find the LCM of the first two, then combine that result with the next number.

Adding fractions with the LCM

The most common school use of the LCM is finding the least common denominator when adding fractions.

Worked example — 1/4 + 1/6:

LCM(4, 6) = 12, so 12 is the least common denominator
1/4 = 3/12
1/6 = 2/12
3/12 + 2/12 = 5/12

Using the LCM rather than just multiplying denominators (which would give 24) keeps the numbers smaller and the answer already close to simplest form.

Where the LCM is used

Adding fractions: the least common denominator is the LCM of the denominators.
Scheduling: if one bus comes every 12 minutes and another every 18, they arrive together every LCM(12, 18) = 36 minutes.
Gears and cycles: the LCM tells you when two rotating parts return to their starting alignment.
Tiling and packing: the LCM gives the smallest square that can be tiled evenly by two different rectangle sizes.

Frequently Asked Questions

What is the least common multiple (LCM)?

The least common multiple of two or more numbers is the smallest positive number that all of them divide into exactly. For example, the LCM of 4 and 6 is 12, because 12 is the smallest number that both 4 and 6 divide evenly.

How do you find the LCM of two numbers?

There are three standard methods. List the multiples of each number and find the first shared one; factorize both into primes and take the highest power of every prime; or use the formula LCM(a, b) = (a × b) ÷ GCF(a, b). For 12 and 18: GCF is 6, so LCM = (12 × 18) ÷ 6 = 36.

What is the LCM formula?

For two numbers, LCM(a, b) = (a × b) ÷ GCF(a, b). This works because the product of two numbers always equals their GCF times their LCM. For three or more numbers, apply the formula in pairs: find the LCM of the first two, then the LCM of that result and the next number.

What is the difference between LCM and GCF?

The LCM is the smallest number that all the given numbers divide into, while the GCF is the largest number that divides all of them. For 12 and 18: the LCM is 36 and the GCF is 6. The LCM is always greater than or equal to the largest input; the GCF is always less than or equal to the smallest.

What is the LCM of two prime numbers?

The LCM of two different prime numbers is simply their product, because they share no factors. For example, LCM(7, 11) = 77. This is the case for any two coprime numbers, whether or not they are prime.

Can the LCM be smaller than the given numbers?

No. The LCM is always greater than or equal to the largest of the given numbers, since it must be a multiple of each one. The LCM equals the largest number when that number is divisible by all the others — for example, LCM(3, 6, 12) = 12.

What is the LCM used for?

The most common use is adding and subtracting fractions with different denominators — you convert both to the least common denominator, which is the LCM of the denominators. It also solves scheduling problems, such as finding when two repeating events coincide.

How do you find the LCM of three or more numbers?

Work in pairs. Find the LCM of the first two numbers, then find the LCM of that result and the third number, and continue through the set. For 4, 6, and 10: LCM(4, 6) = 12, then LCM(12, 10) = 60. So the LCM of all three is 60.

Is "least common factor" the same as LCM?

No — "least common factor" is a common mix-up. The least common factor of any set of numbers is always 1, since 1 divides everything, so the term is not useful. People searching for it usually mean either the least common multiple (LCM) or the greatest common factor (GCF).

What is a least common denominator?

The least common denominator (LCD) is the LCM of the denominators of two or more fractions. To add 1/4 and 1/6, you find LCM(4, 6) = 12, convert to 3/12 and 2/12, then add to get 5/12.