Math calculator

Free least common multiple (LCM) calculator

Find the least common multiple of two or more numbers — enter your numbers to see the LCM and its use in fractions and scheduling, updated live, as you type.

On this page10 sections

InputsLive

Integers (comma-separated)

Enter whole numbers separated by commas or spaces. Non-integers are ignored.

Result

LCM

LCM of 4, 6, 10 = 60

LCM60

GCF2

Count3

Values used4, 6, 10

LCM via |a×b|/GCF, extended to N numbers. Source: Hardy & Wright.

Results are estimates. Consult a professional.

How it's calculated

How the least common multiple calculator works

The least common multiple (LCM) of two or more integers is the smallest positive integer that is divisible by all of them. It is essential for adding fractions with unlike denominators, scheduling repeating events, and working with gear ratios.

Method 1 — via GCF:

LCM(a, b) = |a × b| / GCF(a, b)

Method 2 — prime factorization:

LCM = product of all prime factors at their HIGHEST powers

The GCF-based method is fastest for two numbers. For more than two numbers, compute pairwise: LCM(a, b, c) = LCM(LCM(a, b), c). The prime factorization method is more transparent for small numbers.

Weisstein, Eric W. — Least Common Multiple. MathWorld, Wolfram Research.

Example

Worked example: LCM(12, 18)

Example: LCM(12, 18)

Find the least common multiple of 12 and 18 using both methods.

GCF method:

GCF(12, 18) = 6

LCM(12, 18) = (12 × 18) / 6 = 216 / 6 = 36

Prime factorization check:

12 = 2² × 3¹

18 = 2¹ × 3²

LCM = 2² × 3² = 4 × 9 = 36

LCM(12, 18) = 36

36 is the smallest number that both 12 and 18 divide into evenly — useful for finding a common denominator of 1/12 and 1/18.

Quick reference

LCM for common number pairs

The table below covers the most frequently needed LCM values, particularly for fraction arithmetic.

a	b	GCF(a, b)	LCM(a, b)
4	6	2	12
6	9	3	18
8	12	4	24
12	18	6	36
15	20	5	60
6	10	2	30
14	21	7	42
16	24	8	48

LCM(a, b) = (a × b) / GCF(a, b). These pairs cover the most common fraction denominators in arithmetic.

Practical tips

Tips for finding the least common multiple

LCM comes up constantly in fraction arithmetic and real-world scheduling. These tips make the process faster.

Use the GCF shortcut — always faster than listing multiples by hand; compute GCF first, then divide the product by it.
LCM of coprime numbers is their product — if GCF(a, b) = 1, then LCM(a, b) = a × b; e.g., LCM(7, 9) = 63.
Finding a common denominator — to add ⅓ + ¼, find LCM(3, 4) = 12, then rewrite as 4/12 + 3/12 = 7/12.
Scheduling repeating events — if event A repeats every 4 days and event B every 6 days, they next coincide on day LCM(4, 6) = 12.
GCF × LCM = a × b — this identity lets you cross-check; if GCF(a,b) × LCM(a,b) ≠ a × b, recheck your work.

Accuracy & limits

Accuracy and limitations

This calculator computes LCM exactly using the GCF-based formula for any positive integers within JavaScript's safe integer range (up to 2⁵³ − 1). For very large inputs, the intermediate product a × b can overflow before division; the calculator detects this and uses the safer equivalent LCM(a, b) = (a / GCF(a, b)) × b to avoid overflow. Inputs must be positive integers; LCM is not defined for zero or negative integers in this context.

Glossary

Key terms

The smallest positive integer that is divisible by each of two or more given integers.

The result of multiplying an integer by any positive integer; multiples of 6 are 6, 12, 18, 24, …

The largest integer dividing two numbers exactly; used in the LCM shortcut formula.

Expressing a number as a product of primes; LCM uses the highest power of each prime appearing in any factor.

A shared multiple of two denominators; the LCM of the denominators is the lowest common denominator (LCD).

Two integers with GCF = 1; their LCM equals their product.

About

About this calculator

Part of our math calculators suite — explore all calculators.

Questions

Frequently asked questions about the free least common multiple (LCM) calculator

A least common multiple calculator is a free online tool that helps you find the smallest positive integer that every number in a list divides. Useful for finding a common denominator or repeating schedule. The least common multiple (LCM) is the smallest positive integer that every input divides evenly. It pairs naturally with the greatest common factor (GCF) — once you have the GCF, the LCM follows in one step. It runs entirely in your browser with instant results and no sign-up.

Because a × b can overflow or become huge fast. lcm(40000, 60000) via the formula is (40000 × 60000) ÷ 20000 = 120000, computed safely. Multiplying then dividing by GCF keeps intermediate values small.

Their product. If gcd(a, b) = 1, then lcm(a, b) = a × b / 1 = a × b. So lcm(7, 13) = 91.

LCM is 0. Zero is a multiple of every integer (0 = n × 0), so technically the smallest non-negative common multiple is 0 itself. The calculator returns 0 when any input is 0.