Arithmetic & Numbers

LCM & GCF Calculator

Enter two or more whole numbers separated by commas. The calculator factorises each into primes, then builds the GCF from the shared primes and the LCM from all primes.

Updated October 3, 2026Written and reviewed by Mateuss M.Method: how we calculate

Try an example:

AnswerLCM 36 · GCF 6

GCF (HCF) = 6
LCM = 36

Step-by-step working 4 steps

1
Prime-factorise every number
```
12 = 2² × 3
18 = 2 × 3²
```
Break each number into primes.
2
GCF: take each shared prime at its lowest power
```
2 × 3 = 6
```
Only primes that appear in every number count.
3
LCM: take every prime at its highest power
```
2² × 3² = 36
```
Include every prime that appears in any number.
4
Cross-check
```
GCF × LCM = 6 × 36 = 216
12 × 18 = 216
```
For two numbers the product of GCF and LCM always equals the product of the numbers.

How to use the lcm & gcf calculator

Type your numbers, separated by commas.
Each number is split into prime factors.
The GCF takes the lowest power of each shared prime; the LCM takes the highest power of every prime.
For two numbers, the cross-check line proves the result.

From prime factors

GCF = product of shared primes at their lowest powers
LCM = product of all primes at their highest powers
GCF(a, b) × LCM(a, b) = a × b

HCF (highest common factor) and GCF (greatest common factor) are two names for the same value.

Worked examples

Each example below is generated by the same calculator you used above, so the working always matches the answer.

12 and 18

AnswerLCM 36 · GCF 6

GCF (HCF) = 6
LCM = 36

Step-by-step working 4 steps

1
Prime-factorise every number
```
12 = 2² × 3
18 = 2 × 3²
```
Break each number into primes.
2
GCF: take each shared prime at its lowest power
```
2 × 3 = 6
```
Only primes that appear in every number count.
3
LCM: take every prime at its highest power
```
2² × 3² = 36
```
Include every prime that appears in any number.
4
Cross-check
```
GCF × LCM = 6 × 36 = 216
12 × 18 = 216
```
For two numbers the product of GCF and LCM always equals the product of the numbers.

12, 18 and 30

AnswerLCM 180 · GCF 6

GCF (HCF) = 6
LCM = 180

Step-by-step working 3 steps

1
Prime-factorise every number
```
12 = 2² × 3
18 = 2 × 3²
30 = 2 × 3 × 5
```
Break each number into primes.
2
GCF: take each shared prime at its lowest power
```
2 × 3 = 6
```
Only primes that appear in every number count.
3
LCM: take every prime at its highest power
```
2² × 3² × 5 = 180
```
Include every prime that appears in any number.

8 and 15

AnswerLCM 120 · GCF 1

GCF (HCF) = 1
LCM = 120

Step-by-step working 4 steps

1
Prime-factorise every number
```
8 = 2³
15 = 3 × 5
```
Break each number into primes.
2
GCF: take each shared prime at its lowest power
```
No shared primes → GCF = 1
```
Only primes that appear in every number count.
3
LCM: take every prime at its highest power
```
2³ × 3 × 5 = 120
```
Include every prime that appears in any number.
4
Cross-check
```
GCF × LCM = 1 × 120 = 120
8 × 15 = 120
```
For two numbers the product of GCF and LCM always equals the product of the numbers.

48, 180

AnswerLCM 720 · GCF 12

GCF (HCF) = 12
LCM = 720

Step-by-step working 4 steps

1
Prime-factorise every number
```
48 = 2⁴ × 3
180 = 2² × 3² × 5
```
Break each number into primes.
2
GCF: take each shared prime at its lowest power
```
2² × 3 = 12
```
Only primes that appear in every number count.
3
LCM: take every prime at its highest power
```
2⁴ × 3² × 5 = 720
```
Include every prime that appears in any number.
4
Cross-check
```
GCF × LCM = 12 × 720 = 8640
48 × 180 = 8640
```
For two numbers the product of GCF and LCM always equals the product of the numbers.

Common mistakes to avoid

Mixing up LCM and GCF

GCF is never larger than the smallest number; LCM is never smaller than the largest. If your answer breaks that rule, you swapped them.

Multiplying the numbers to get the LCM

a × b is a common multiple but only the least one when the numbers share no factors.

Missing a repeated prime

12 = 2 × 2 × 3, so the prime 2 counts twice. Use exponents to keep track.

Frequently asked questions

When do I use LCM versus GCF?

Use the LCM when events repeat on cycles or when you need a common denominator. Use the GCF when you are splitting into equal groups or simplifying a fraction.

What is the largest number allowed?

Up to one billion per number. Beyond that the factorization is slow in a browser.