Two numbers: LCM of 4 and 6
- Input
- Numbers = 4, 6
- Working
- Multiples of 4: 4, 8, 12, 16… Multiples of 6: 6, 12, 18… The first multiple in both lists is 12. Check with the shortcut: (4 × 6) / GCF(4, 6) = 24 / 2 = 12.
- Result
- LCM(4, 6) = 12
Find the least common multiple of two or more numbers using prime factors or listing multiples, with the shared multiples highlighted in the working. Runs entirely in your browser — your numbers never leave this device.
| Number | Prime factorisation |
|---|---|
| 4 | 4 = 2² |
| 6 | 6 = 2 × 3 |
| 8 | 8 = 2³ |
The least common multiple is the smallest number that every one of your numbers divides into exactly. The calculator finds it by prime factorisation: each number is broken into primes, the highest power of each prime across all the numbers is kept, and those powers are multiplied together. For 4, 6 and 8 that means 4 = 2², 6 = 2 × 3 and 8 = 2³, so the LCM takes 2³ (from the 8) and 3¹ (from the 6): 8 × 3 = 24.
The working also lists the first few multiples of each number, because for small inputs that is the fastest way to see the answer — the LCM is simply the first multiple that appears in every list. For two numbers there is a shortcut worth knowing: LCM(a, b) = (a × b) / GCF(a, b), which the calculator uses as an independent check on the factorisation result.
Signs are ignored (the LCM of −4 and 6 is the same as the LCM of 4 and 6), and a single number's LCM is the number itself. Zero is the one special case: by convention the LCM of any number and 0 is 0, since 0 is the only multiple of 0 — the calculator reports this rather than hunting forever for a positive common multiple that does not exist.
Its most common job is adding and subtracting fractions: the LCM of the denominators is the common denominator, so LCM(4, 6) = 12 turns 1/4 + 1/6 into twelfths. It also answers scheduling questions — if one bus runs every 4 days and another every 6, they coincide every 12 days — and any problem where cycles of different lengths must line up.
They are opposites in spirit. The GCF is the largest number that divides into all your numbers (it is never bigger than the smallest of them); the LCM is the smallest number that all your numbers divide into (it is never smaller than the largest of them). For two numbers they are linked: LCM × GCF = the product of the two numbers, as in 12 × 2 = 4 × 6.
Coprime numbers share no prime factors, so a common multiple must contain every prime factor of both numbers at full strength — nothing can be shared or overlapped. The smallest such number is exactly the product, which is why LCM(5, 7) = 35 and LCM(4, 9) = 36.
Yes — enter three or more numbers and the prime factor method handles them together, taking the highest power of each prime across the whole set. Doing it by hand, the reliable route is pairwise: find the LCM of the first two, then find the LCM of that result and the next number, and repeat.
With 1, nothing changes: the LCM is the LCM of the remaining numbers, since every number is a multiple of 1 in the sense required — LCM(1, 6) = 6. With 0, the answer is 0 by convention, because 0 is the only multiple of 0, so it is the only common multiple available.
No. It runs 100% in your browser, so the numbers you enter are processed locally on your device and are never uploaded, stored or shared with anyone.
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