LCM & HCF Calculator
Find the LCM and HCF (GCD) of two or more numbers instantly, with prime factorization shown for up to 4 numbers to explain the answer.
About the LCM & HCF Calculator
This LCM and HCF calculator finds the least common multiple and the highest common factor (also called GCD, the greatest common divisor) of any list of positive whole numbers — not just two. Type or paste the numbers separated by commas, spaces or new lines and both answers appear instantly.
For up to four numbers, the tool also displays each number's prime factorization (12 = 2² × 3), the method taught in school: the HCF takes the lowest power of every common prime, while the LCM takes the highest power of every prime that appears in any number.
LCM answers "when do repeating events coincide?" — bus timetables, gear rotations, adding fractions with unlike denominators. HCF answers "what is the largest equal grouping?" — cutting ribbons into equal pieces or reducing fractions and ratios. Both are computed exactly using the Euclidean algorithm, so even large numbers are instant.
How to Use the LCM & HCF Calculator
- 1Enter two or more positive whole numbers, separated by commas, spaces or new lines.
- 2Read the LCM and HCF instantly.
- 3For up to 4 numbers, review the prime factorization of each to see why.
- 4Add more numbers to the list any time — the results update live.
Frequently Asked Questions
What is the difference between LCM and HCF?
The HCF (highest common factor, same as GCD) is the largest number that divides all the given numbers exactly — for 12 and 18 it is 6. The LCM (least common multiple) is the smallest number that all of them divide into — for 12 and 18 it is 36. HCF is always ≤ the smallest input; LCM is always ≥ the largest input.
How do you find LCM and HCF using prime factorization?
Write each number as a product of prime powers: 12 = 2² × 3 and 18 = 2 × 3². For the HCF take the lowest power of each common prime: 2 × 3 = 6. For the LCM take the highest power of every prime present: 2² × 3² = 36. This calculator shows those factorizations for up to four numbers so you can verify each step.
Is HCF the same as GCD and GCF?
Yes — HCF (highest common factor), GCD (greatest common divisor) and GCF (greatest common factor) are three names for exactly the same thing. HCF is the common term in Indian and British textbooks, while GCD and GCF are more common in American materials and computer science. This calculator's HCF result answers all three.
Does LCM × HCF equal the product of the numbers?
For exactly two numbers, yes: LCM(a, b) × HCF(a, b) = a × b, a handy identity for checking answers — 36 × 6 = 216 = 12 × 18. The identity does not extend to three or more numbers, which is why this calculator computes the LCM iteratively as lcm(lcm(a, b), c) rather than from the product.
Where is LCM used in real life?
Anywhere repeating cycles must line up: two buses leaving every 12 and 18 minutes depart together every 36 minutes (the LCM). It is also the least common denominator when adding fractions, and it appears in gear ratios, planning shift rotations and tiling problems. HCF conversely finds the largest tile, ribbon length or group size that fits everything evenly.