HCF and LCM Calculator (GCF) | Find HCF & LCM Instantly
Use this HCF and LCM calculator to instantly find the highest common factor (HCF) and least common multiple (LCM) of any numbers. This free GCF calculator provides fast and accurate results with step-by-step explanations, making it easy to calculate HCF online and find LCM and GCF in seconds. Try it now to solve math problems quickly and easily.
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What is HCF (Highest Common Factor)?
The highest common factor (HCF), also known as the greatest common factor (GCF) or highest common divisor, is the largest number that divides two or more numbers exactly.
Example:
- HCF of 12 and 18 = 6
- HCF of 24 and 32 = 8
You can use this highest common factor calculator or common factor calculator to find results instantly.
What is LCM (Least Common Multiple)?
The least common multiple (LCM) is the smallest number that is divisible by two or more numbers.
Example:
- LCM of 3 and 9 = 9
- LCM of 5 and 10 = 10
This least common multiple calculator helps you find accurate results quickly.
HCF and LCM Calculator (How It Works)
This HCF LCM calculator works as a complete:
- GCF and LCM finder
- calculator for LCM and GCF
- greatest common factor and least common multiple calculator
Just enter numbers and get:
- HCF (GCF)
- LCM
- Step-by-step solution
How to Find HCF and LCM (Step-by-Step)​
Method 1:
Prime Factorization Method
- Write prime factors of numbers
- Find common factors → HCF
- Multiply all factors → LCM
Method 2:
Formula Method
LCM = (Number1 × Number2) ÷ HCF
Examples of HCF and LCM
Here is a quick HCF and LCM table for commonly asked examples:
| HCF Examples (With Answers) | HCF | LCM Examples (Solved) | LCM |
|---|---|---|---|
| 12 & 18 | 6 | 3 & 9 | 9 |
| 24 & 32 | 8 | 4 & 6 | 12 |
| 16 & 20 | 4 | 5 & 10 | 10 |
| 8 & 12 | 4 | 6 & 8 | 24 |
| 15 & 25 | 5 | 7 & 14 | 14 |
| 21 & 28 | 7 | 9 & 15 | 45 |
| 14 & 49 | 7 | 10 & 20 | 20 |
| 18 & 27 | 9 | 12 & 18 | 36 |
| 20 & 30 | 10 | 8 & 12 | 24 |
| 36 & 48 | 12 | 14 & 21 | 42 |
| 45 & 60 | 15 | 15 & 25 | 75 |
| 50 & 100 | 50 | 16 & 20 | 80 |
| 81 & 27 | 27 | 18 & 24 | 72 |
| 72 & 54 | 18 | 20 & 30 | 60 |
| 64 & 16 | 16 | 21 & 28 | 84 |
| 99 & 33 | 33 | 24 & 32 | 96 |
| 100 & 40 | 20 | 25 & 40 | 200 |
| 56 & 98 | 14 | 27 & 36 | 108 |
| 35 & 70 | 35 | 30 & 45 | 90 |
| 48 & 180 | 12 | 35 & 50 | 350 |
Why Use This HCF LCM Calculator?
- Fast and accurate results
- Works as GCF LCM calculator
- Easy to use
- Step-by-step explanation
- 100% free online tool
Real-Life Uses of HCF and LCM
- Fractions simplify karna
- Time problems solve karna
- School math problems
- Engineering calculations
HCF and LCM Table (With Examples)
The following HCF and LCM table shows the highest common factor (HCF) and least common multiple (LCM) of commonly used number pairs. This table helps you quickly understand how to find HCF and LCM in math problems.
| Numbers | HCF (Highest Common Factor) | LCM (Least Common Multiple) |
|---|---|---|
| 4 & 8 | 4 | 8 |
| 5 & 10 | 5 | 10 |
| 12 & 18 | 6 | 36 |
| 24 & 32 | 8 | 96 |
| 6 & 9 | 3 | 18 |
| 8 & 12 | 4 | 24 |
| 7 & 14 | 7 | 14 |
| 9 & 15 | 3 | 45 |
| 10 & 20 | 10 | 20 |
| 14 & 21 | 7 | 42 |
| 15 & 25 | 5 | 75 |
| 16 & 20 | 4 | 80 |
| 18 & 24 | 6 | 72 |
| 20 & 30 | 10 | 60 |
| 21 & 28 | 7 | 84 |
| 24 & 36 | 12 | 72 |
| 25 & 40 | 5 | 200 |
| 27 & 36 | 9 | 108 |
| 30 & 45 | 15 | 90 |
| 35 & 50 | 5 | 350 |
How to use this table?
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Find your numbers in the table to get the HCF (GCF) and LCM instantly. If your numbers are not listed, use the HCF and LCM calculator above.
Frequently Asked Questions
What is HCF (Highest Common Factor)?
The HCF (highest common factor), also called the GCF (greatest common factor), is the largest number that divides two or more numbers exactly without leaving a remainder.
What is LCM (Least Common Multiple)?
The LCM (least common multiple) is the smallest number that is exactly divisible by two or more given numbers.
What is the difference between HCF and LCM?
The HCF is the largest common divisor, while the LCM is the smallest common multiple of given numbers.
How to find HCF easily?
You can find HCF using:
- Prime factorization method
- Division method
Or use an online HCF calculator for instant results.
How to find LCM quickly?
The easiest way to find LCM is by using the formula:
LCM = (a × b) ÷ HCF
You can also use a least common multiple calculator for fast results.
What is GCF in math?
The GCF (greatest common factor) is another name for HCF and represents the largest number that divides given numbers.
Can I calculate HCF and LCM online?
Yes, you can use this HCF and LCM calculator online to quickly find accurate results with step-by-step explanations.
What are common factors?
Common factors are numbers that divide two or more numbers exactly. The highest of these is called the HCF.
What are common multiples?
Common multiples are numbers that are divisible by two or more numbers. The smallest of these is called the LCM.
Why is HCF important?
The HCF helps simplify fractions, solve math problems, and find the greatest shared value between numbers.
Why is LCM used?
The LCM is used in solving problems involving time intervals, fractions, and finding common denominators.
What is the HCF of 12 and 18?
The HCF of 12 and 18 is 6.
What is the LCM of 3 and 9?
The LCM of 3 and 9 is 9.
What is the HCF of 24 and 32?
The HCF of 24 and 32 is 8.
What is the LCM of 9 and 15?
The LCM of 9 and 15 is 45.