Free AI LCM and HCF Calculator
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How LCM and HCF Calculator Works
Our Free LCM and HCF Calculator is the perfect tool for students, teachers, and professionals to easily calculate the Least Common Multiple (LCM) and Highest Common Factor (HCF) of any set of positive integers in seconds.
Whether you’re solving math problems, preparing for exams, or simply need to find the LCM and HCF for a real-world situation, this tool helps you get quick and accurate results. It not only gives you the answers but also shows step-by-step solutions to make sure you understand the process clearly.
Here’s how it works: Simply enter the numbers you want to calculate, and choose whether you need the Least Common Multiple (LCM) or Highest Common Factor (HCF). The calculator will instantly display the result, and provide you with detailed steps, helping you understand the logic behind the calculation.
Our calculator supports multiple numbers (not just two), and uses the Euclidean algorithm for HCF and the prime factorization method for LCM. This ensures that the results are accurate and reliable, whether you’re working with small numbers or large ones.
Say goodbye to manual calculations and errors – with our Free Online LCM and HCF Calculator, you can save time and avoid mistakes. Try it today and experience how easy math can be!
How to Use LCM and HCF Calculator Online
- Enter two or more positive integers in the input box, separated by commas or spaces.
- Click on the "Calculate" button to instantly get the LCM and HCF results.
- View the LCM and HCF values displayed in the results section below.
- Study the step-by-step breakdown to understand how the results were derived and which methods were used.
- If you need to start fresh, use the "Reset" button to clear all inputs and results.
- Try the "Example" buttons for quick demonstrations and better understanding.
What is LCM in Maths with Example?
The LCM (Least Common Multiple) in Mathematics. is the smallest positive number that is exactly divisible by two or more given numbers without leaving any remainder.
For example, the LCM of 4 and 6 is 12, because 12 is the smallest number that can be divided by both 4 and 6 completely.
Uses of LCM in Real Life
- To find a common denominator while adding or subtracting fractions.
- To calculate when two or more repeating events will happen together — like bus or train timings.
- Useful in solving time and work-related mathematical problems.
- Helps in scheduling tasks or planning events that need to align at specific intervals.
What is HCF in Maths with Examples?
The Highest Common Factor (HCF) in maths is the greatest number that can exactly divide two or more given numbers without leaving any remainder. It is also called the Greatest Common Divisor (GCD).
For example, the HCF of 12 and 18 is 6, because 6 is the largest number that divides both 12 and 18 completely.
Uses of HCF in Real Life:
- To simplify fractions to their lowest terms easily.
- To divide things into the largest possible equal groups.
- Helpful in reducing ratios to their simplest form.
- Used in problems related to measurements — like finding the biggest size of tiles to cover a floor without cutting.
- Finding the greatest common unit to measure different quantities.
Difference Between LCM and HCF with Examples (Comparison Table)
The main difference between LCM and HCF is that LCM is the smallest number that is divisible by all given numbers, while HCF is the largest number that divides all given numbers completely.
| Aspect | LCM (Lowest Common Multiple) | HCF (Highest Common Factor) |
|---|---|---|
| Definition | Smallest number divisible by all given numbers | Largest number that divides all given numbers |
| Value Range | Always greater than or equal to the largest number in the set | Always less than or equal to the smallest number in the set |
| Methods of Finding | Prime factorization, Listing multiples, Using HCF | Prime factorization, Euclidean algorithm, Factorization |
| Connection to Numbers | Common Multiple | Common Divisor |
| Common Application | Finding common denominators in fractions | Simplifying fractions |
| Relationship | LCM × HCF = Product of the numbers (for two numbers) | |
LCM and HCF are two important concepts in mathematics used for solving problems related to multiples and factors.
LCM and HCF Formula Used in Calculation
To calculate LCM (Least Common Multiple) and HCF (Highest Common Factor) of two numbers (a and b), the following formulas and methods are commonly used.
LCM × HCF = a × b
This is the most popular formula for LCM and HCF calculation. It means the product of the LCM and HCF of two numbers is equal to the product of those numbers.
How to Calculate LCM Using Prime Factorization Method:
- Find the prime factors of each number.
- Select each prime factor with the highest power.
- Multiply all selected prime factors to get the LCM.
How to Calculate HCF using Euclidean Algorithm:
HCF(a, b) = HCF(b, a mod b)
Repeat this process until the remainder becomes 0. The last non-zero number is the HCF (Highest Common Factor) of the given numbers.
You can easily use the above LCM and HCF formulas and methods to calculate results manually or with the help of our LCM HCF Calculator given above.
LCM and HCF Examples
Example 1: Find the LCM and HCF of 12 and 18
Solution:
Finding HCF using Euclidean Algorithm:
- Divide 18 by 12 → 18 = 12 × 1 + 6
- Divide 12 by 6 → 12 = 6 × 2 + 0
- Since remainder is 0, HCF = 6
Finding LCM using HCF Formula:
LCM = (12 × 18) ÷ 6 = 216 ÷ 6 = 36
Final Answer: HCF = 6 and LCM = 36
Example 2: Find the LCM and HCF of 15, 25, and 35
Solution:
Finding HCF using Prime Factorization Method:
- 15 = 3 × 5
- 25 = 5 × 5
- 35 = 5 × 7
Common prime factor = 5
Finding LCM using Prime Factors:
Final Answer: HCF = 5 and LCM = 525
Example 3: Find the LCM and HCF of 8, 9, and 25
Solution:
Finding HCF:
- 8 = 2 × 2 × 2
- 9 = 3 × 3
- 25 = 5 × 5
No common prime factor is available.
Finding LCM:
Final Answer: HCF = 1 and LCM = 600
Methods of Finding LCM and HCF
How to Find LCM and HCF Using Prime Factorization
For HCF: Break each number into its prime factors. Then, multiply the common prime factors with the smallest powers. This will give the HCF.
For LCM: Multiply all prime factors that appear in any of the numbers. Use the highest powers of the common factors.
Example: Find HCF and LCM of 24 and 36
- Prime factors of 24 = 2×2×2×3
- Prime factors of 36 = 2×2×3×3
HCF = 2×2×3 = 12
LCM = 2×2×2×3×3 = 72
How to Find LCM and HCF of Fractions
To find LCM of fractions:
- LCM = LCM of Numerators / HCF of Denominators
- HCF = HCF of Numerators / LCM of Denominators
Example: Find LCM of 2/3 and 5/6
- LCM of Numerators = LCM(2,5) = 10
- HCF of Denominators = HCF(3,6) = 3
LCM = 10/3
How to Find LCM and HCF (Class 10 level)
At Class 10 level, students generally use the Division Method for HCF and either the Prime Factorization Method or Division Method for LCM.
Division Method for HCF: Divide the larger number by the smaller number. Continue dividing the remainder till it becomes 0. The last non-zero remainder is the HCF.
Example: Find HCF of 42 and 56 using Division Method
- 56 ÷ 42 = 1 remainder 14
- 42 ÷ 14 = 3 remainder 0
HCF = 14
How to Find LCM and HCF of Two Numbers
To find the LCM and HCF of two numbers, either use Prime Factorization or Division Method as explained above. Also, you can use this formula:
Formula: LCM × HCF = Product of the two numbers
Example: Find LCM of 21 and 28 if HCF is 7
LCM = (21×28) ÷ 7 = 588 ÷ 7 = 84
How to Find LCM and HCF of Three Numbers
To calculate the HCF of three numbers, first determine the HCF of any two numbers. Then, find the HCF of that result with the third number.
For LCM, follow the same process using LCM calculations.
Example: Find HCF and LCM of 15, 25, and 35
HCF = 5
LCM = 3×5×5×7 = 525