Both answers at once
LCM and GCF come from the same prime factorisation, so there is no reason to run two separate calculators. Enter your numbers once and get both.
LCM and GCF Calculator – With Step by Step Working
Enter two or more numbers and get the least common multiple and the greatest common factor instantly, along with the working your teacher wants to see: prime factorisation with exponents, the ladder (division) method, Euclid’s algorithm, full factor lists and the first common multiples.
LCM & GCF togetherUp to 10 numbersThree methods shownAlso called HCF & LCDWorks offline
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Least common multiple (LCM)
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Greatest common factor (GCF / HCF)
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What this LCM and GCF calculator gives you
Getting the answer is easy. Showing the method is what marks are given for, so this calculator writes out the working three different ways and lets you use whichever one your class was taught.
Real step-by-step working
Prime factors with exponents, the highest and lowest powers picked out, and a written explanation of why each factor was chosen – not just a number in a box.
The ladder method too
The division ladder that most schools teach is drawn as a proper table, with the divisor column highlighted so you can copy it straight into your book.
Euclid’s algorithm
Every remainder step is listed for the GCF, which is the method you need for large numbers and for exams that ask for the Euclidean approach.
Up to ten numbers
Most calculators stop at two or three. This one handles a whole list, and still shows the factor table for every value you enter.
Instant and private
Everything is calculated in your browser as you type. No adverts in the way, no sign-up, and it keeps working with the connection off.
How to find the LCM and GCF
Enter your numbers
Type two or more whole numbers separated by commas or spaces. Decimals and negatives are not used for LCM and GCF, so the tool asks you to correct them.
Read the two answers
The orange card is the least common multiple and the slate card is the greatest common factor, also written as HCF or GCD depending on your syllabus.
Open the prime factors tab
Each number is broken into primes. Take the highest power of every prime for the LCM, and the lowest power of the primes that all numbers share for the GCF.
Or use the ladder
Divide the whole row by a prime that goes into every number, write the quotients underneath and repeat. The divisors multiply to the GCF; divisors plus the bottom row multiply to the LCM.
Check with Euclid
For two numbers, divide the larger by the smaller and keep replacing the pair with the divisor and remainder. The last non-zero remainder is the GCF.
Copy your answer
Use the copy button to take the result and the key working with you into your homework or notes.
LCM and GCF in plain English
Least common multipleThe smallest number that every one of your numbers divides into exactly.
LCM(4, 6) = 12Greatest common factorThe largest number that divides exactly into all of them.
GCF(12, 18) = 6Other namesGCF is also called HCF (highest common factor) or GCD (greatest common divisor). LCM is called LCD when it is used as a denominator.
The key identityFor any two numbers,
GCF x LCM = a x b. It is the fastest way to check your answer.Coprime numbersIf the GCF is 1 the numbers share no factors, and the LCM is simply their product.
LCM(7, 13) = 91Where they are usedGCF simplifies fractions; LCM finds the common denominator when you add or subtract them.
When you need them
- Add or subtract fractions by finding the lowest common denominator.
- Simplify a fraction all the way down in one step using the GCF.
- Work out when two repeating events line up again, such as buses, shifts or planets.
- Split items into the largest possible equal groups with nothing left over.
- Find gear ratios, tiling patterns and packaging sizes that fit exactly.
- Check homework answers and see exactly where a step went wrong.
- Reduce ratios and rates to their simplest form.
LCM and GCF FAQ
The GCF is the largest number that divides into all of your numbers, so it is never bigger than the smallest one. The LCM is the smallest number that all of them divide into, so it is never smaller than the largest one. GCF makes numbers smaller and is used to simplify; LCM makes them bigger and is used to find a common denominator.
Yes. Greatest common factor, highest common factor and greatest common divisor are three names for the same value. American textbooks usually say GCF, British and Indian syllabuses say HCF, and computer science and number theory tend to use GCD. This calculator gives the same answer whichever name your course uses.
Break every number into prime factors written with exponents, then take the highest power of each prime that appears anywhere and multiply them together. For 12 = 2 squared times 3 and 18 = 2 times 3 squared, you take 2 squared and 3 squared, giving 36. For the GCF you instead take the lowest power of only the primes that appear in every number, which gives 6.
Write your numbers in a row and divide the whole row by a prime that goes into every one of them, writing the quotients underneath. Repeat until no prime divides them all. Multiplying the divisors down the left gives the GCF, and multiplying those divisors by everything left in the bottom row gives the LCM. It is the fastest method to do by hand for two or three numbers.
Yes, and it happens whenever the numbers share no prime factors at all. Such numbers are called coprime or relatively prime, and their LCM is simply the product of the numbers. Any two consecutive whole numbers, and any two different primes, are always coprime.
For two numbers, multiply the GCF by the LCM. The result should equal the two numbers multiplied together. You can also check that the LCM divides exactly by each number and that each number divides exactly by the GCF. The calculator runs both checks for you and shows them beside the answers.
Yes, for up to ten numbers at once. The LCM and GCF of a list are found by taking them two at a time: work out the answer for the first pair, then combine that with the next number, and so on. The prime factor table and ladder shown here handle the whole list together.
LCM and GCF are defined for positive whole numbers, so this tool asks for those. If you have decimals, multiply each one by the same power of ten first, work out the answer, then divide back. Negative numbers are usually handled by taking the absolute value, since factors are conventionally written as positive.
Get the answer and the working
Two numbers or ten, prime factors, ladder and Euclid, all in one screen. Free, unlimited and calculated on your own device.