What is the least common multiple?

The LCM of a set of numbers is the smallest positive number that appears in every one of their times tables. The LCM of 4 and 6 is 12.

How do you find the LCM with prime factorization?

Factor each number into primes, then take every prime that appears anywhere — at the highest power any one number uses — and multiply them together. For 4 = 2² and 6 = 2 × 3 that gives 2² × 3 = 12.

When do I need the LCM?

Adding or comparing fractions with different denominators (the common denominator is an LCM), scheduling events that repeat on different cycles, and anything where separate rhythms need to line up.

Can the LCM be one of the input numbers?

Yes — whenever one number divides another, the larger one is the LCM. The LCM of 3 and 12 is simply 12.

Arithmetic & Factors

LCM Calculator

The smallest number that every input divides into — worked out by prime factorization, with a listing check you can verify by eye.

Your numbers

Numbers to compare

2 numbers recognised

Two to four whole numbers between 1 and 100,000.

Worked solution

LCM of 4, 6

The smallest number every one of them divides into

12 is the first number that appears in the times table of every input — found by taking each prime at its highest needed power.

The working

3 steps

Prime-factor each number
4
2²
6
2 × 3
Take each prime at its highest power
The LCM must be divisible by every number, so each prime appears as many times as its most demanding factorization requires.
Prime In 4 In 6 Use
2 2² 2 2²
3 — 3 3
Multiply those together
LCM = 2² × 3 = 12
Number Its multiples up to the LCM
4 4, 8, 12
6 6, 12
Every list lands on 12 — and on nothing smaller.

Prime	In 4	In 6	Use
2	2²	2	2²
3	—	3	3

Number	Its multiples up to the LCM
4	4, 8, 12
6	6, 12

Works instantly in your browser — nothing is uploaded, and the URL keeps your numbers so you can share the exact worked example.

Listing vs factorization

For small numbers, listing multiples works fine: 4 → 4, 8, 12… and 6 → 6, 12… meet at 12. For bigger numbers the lists get long fast, which is why this calculator uses prime factorization — it jumps straight to the answer by asking, for each prime, how many copies the most demanding number needs.