Least Common Multiple (LCM) Calculator
Find the least common multiple of two or more numbers, with the prime factorization of each number and the step-by-step GCF method used to reach the answer.
Least Common Multiple
84
Result
LCM(4, 6, 14) = 84
What is the Least Common Multiple?
The least common multiple (LCM), also called the lowest common multiple, of two or more integers is the smallest positive integer that all of them divide into evenly. For example, the LCM of 4 and 6 is 12, since 12 is the smallest number that's a multiple of both 4 (4×3) and 6 (6×2).
LCM shows up constantly in everyday math: it's how you find a common denominator when adding or subtracting fractions, and it's used to figure out when two repeating cycles — like bus schedules, blinking lights, or recurring events on different intervals — will next line up at the same time.
Prime Factorization of Each Number
Breaking each number into its prime factors is the most reliable general method for finding the LCM of any list of numbers.
| Number | Prime Factorization |
|---|---|
| 4 | 4 = 2 × 2 |
| 6 | 6 = 2 × 3 |
| 14 | 14 = 2 × 7 |
Step-by-Step: The GCF Method
This calculator combines numbers two at a time using LCM(a, b) = (a × b) ÷ GCF(a, b), then folds the running result in with each remaining number.
| Running LCM | Next Number | GCF | New LCM |
|---|---|---|---|
| 4 | 6 | 2 | 12 |
| 12 | 14 | 2 | 84 |
Three Ways to Find the LCM
Listing multiples — write out multiples of each number until you find one they share. It works for small numbers but becomes tedious and impractical for larger ones.
Prime factorization — break each number into its prime factors, then multiply together the highest power of every prime that appears in any of the numbers. For example, 21 = 3 × 7, 14 = 2 × 7, and 38 = 2 × 19, so LCM(21, 14, 38) = 2 × 3 × 7 × 19 = 798.
GCF method — for two numbers, LCM(a, b) = (a × b) ÷ GCF(a, b). For more than two numbers, find the LCM of the first two, then use that result together with the next number, repeating until every number has been folded in. This is the method used in the step-by-step table above.
Why LCM and GCF Are Related
For any two positive integers, their LCM and GCF (greatest common factor) are linked by a simple identity: LCM(a, b) × GCF(a, b) = a × b. That's why dividing the product of two numbers by their GCF always gives the LCM directly — it's often the fastest method once you already know (or can quickly compute) the GCF.
Example — Your Current Inputs
LCM(4, 6, 14) = 84
Additional Example — Three Numbers
Find LCM(21, 14, 38). First, GCF(21, 14) = 7, so LCM(21, 14) = (21 × 14) ÷ 7 = 42. Next, GCF(42, 38) = 2, so LCM(42, 38) = (42 × 38) ÷ 2 = 798. Checking with prime factorization: 21 = 3 × 7, 14 = 2 × 7, 38 = 2 × 19 — the LCM needs one 2, one 3, one 7, and one 19, giving 2 × 3 × 7 × 19 = 798, confirming the result.
About This Calculator
- Numbers
- Enter two or more positive whole numbers, separated by commas, spaces, or new lines. The calculator finds the LCM across the entire list at once, not just pairs.
Frequently Asked Questions
What is the LCM used for in real life?
The most common use is finding a common denominator when adding or subtracting fractions with different denominators. It's also used for scheduling problems — figuring out when two events on different repeating cycles (like two buses on different routes, or blinking lights with different intervals) will next coincide.
What is the LCM of two prime numbers?
Since two different prime numbers share no common factors other than 1, their LCM is simply their product. For example, LCM(5, 7) = 35.
Can the LCM ever be smaller than the largest input number?
No — the LCM is always greater than or equal to the largest number in the list. It equals the largest number exactly when every other number divides evenly into it (for example, LCM(4, 8) = 8).
How is LCM different from GCF?
GCF (greatest common factor) is the largest number that divides evenly into all the inputs, while LCM is the smallest number that all the inputs divide evenly into. They're opposite in direction — GCF looks for a shared factor, LCM looks for a shared multiple — but they're mathematically linked through the identity LCM(a,b) × GCF(a,b) = a × b.