LCM & HCF Calculator – Find Lowest Common Multiple & Highest Common Factor

Find the Lowest Common Multiple (LCM) and Highest Common Factor (HCF) of any set of numbers instantly with our LCM & HCF Calculator. Whether you're solving math problems, working on ratios, or analyzing data, this dual-function tool calculates both LCM and HCF (also known as GCD or GCF) quickly and accurately.

It supports two or more numbers, handles large integers, and displays step-by-step results making it ideal for students, teachers, and professionals alike.

What Are LCM and HCF?

Before using the calculator, let’s clarify the two key concepts:

HCF (Highest Common Factor)

The HCF (also called GCF or GCD) of two or more numbers is the largest number that divides all of them exactly (without leaving a remainder).

Example:

HCF of 18 and 24 = 6

(because 6 is the largest number that divides both 18 and 24)

LCM (Lowest Common Multiple)

The LCM of two or more numbers is the smallest number that is a multiple of all of them.

Example:

LCM of 4 and 5 = 20

(because 20 is the smallest number divisible by both 4 and 5)

Together, these two values are foundational in arithmetic, algebra, and real-world problem solving — from fractions to scheduling and engineering.

LCM & HCF Calculator Quick, Smart, and Accurate

Our LCM & HCF Calculator automatically determines both values simultaneously. Simply:

1. Enter two or more numbers separated by commas (e.g., 12, 18, 30).
2. Click Calculate.
3. Get instant results for HCF (GCF) and LCM, along with step-by-step explanations.

Example Inputs

Formula for Finding HCF and LCM

HCF Formula (Using Prime Factorization)

To find the HCF:

• Express each number as a product of prime factors.
• Multiply the lowest powers of common primes.

Example:

Find HCF of 12 and 18

12 = 2² × 3¹
18 = 2¹ × 3²

Common primes = 2¹ × 3¹ = 6

HCF = 6

LCM Formula (Using Prime Factorization)

To find the LCM:

• Express each number as a product of primes.
• Multiply the highest powers of all primes that appear.

Example:

Find LCM of 12 and 18
12 = 2² × 3¹
18 = 2¹ × 3²
LCM = 2² × 3² = 36

Relation Between LCM and HCF

For any two numbers a and b:

LCM × HCF = a × b

Example:

For 12 and 18:

LCM × HCF = 36 × 6 = 216

a × b = 12 × 18 = 216

This is one of the most important number theory relationships and our calculator applies it automatically for cross-verification.

Step-by-Step Examples

Example 1: Find HCF and LCM of 8 and 12

Step 1: Prime Factorization

8 = 2³
12 = 2² × 3

Step 2:

HCF = 2² = 4
LCM = 2³ × 3 = 24

Result: HCF = 4, LCM = 24

Example 2: Find HCF and LCM of 15 and 25

Prime Factorization:

15 = 3 × 5
25 = 5²

HCF = 5
LCM = 3 × 5² = 75

Result: HCF = 5, LCM = 75

Example 3: Find HCF and LCM of 12, 18, and 24

Prime Factorization:

12 = 2² × 3¹
18 = 2¹ × 3²
24 = 2³ × 3¹

HCF = 2¹ × 3¹ = 6

LCM = 2³ × 3² = 72

Result: HCF = 6, LCM = 72

Example 4: Find HCF and LCM of 9 and 6

9 = 3²

6 = 2 × 3

HCF = 3

LCM = 2 × 3² = 18

Result: HCF = 3, LCM = 18

Relationship Between HCF and LCM

The relationship between the two is inverse and complementary:

• The HCF finds the largest shared factor.
• The LCM finds the smallest shared multiple.

The formula linking them is:

HCF(a, b) × LCM(a, b) = a × b

This means if you know any two of these values, you can always find the third.

Methods to Find HCF and LCM

1. Prime Factorization Method

Break each number into its prime factors, then:

• Take the lowest power for HCF.
• Take the highest power for LCM.

2. Division Method

For HCF:

1. Divide the larger number by the smaller.
2. Replace the larger number with the remainder.
3. Repeat until remainder = 0.
4. The divisor is the HCF.

For LCM:

Use the relation LCM × HCF = Product of Numbers.

3. Listing Method (For Small Numbers)

List multiples and common factors of the given numbers.

The largest common factor = HCF.

The smallest common multiple = LCM.

Practical Applications of LCM and HCF

LCM and HCF appear in countless real-world scenarios. Here are a few practical examples:

1. Time and Scheduling

To find when two events coincide again.

Example: A bell rings every 12 minutes, another every 15 minutes.

LCM(12, 15) = 60 → They ring together every 60 minutes.

2. Fractions and Ratios

Used to simplify, add, or subtract fractions.
HCF → simplifies numerators and denominators.
LCM → finds a common denominator.

3. Engineering and Design

Used to synchronize repetitive processes and machine cycles.

4. Mathematics and Number Theory

LCM and HCF are key in algebraic simplification and solving Diophantine equations.

5. Real-Life Problem Solving

Helps in dividing resources equally (HCF) or planning combined cycles (LCM).

Comparison Between LCM and HCF

How to Use the LCM & HCF Calculator

Follow these simple steps to find both values instantly:

1. Enter Numbers: Type in two or more numbers separated by commas (e.g., 8, 12, 20).
2. Click "Calculate": The calculator finds both HCF and LCM automatically.
3. View Step-by-Step Solution: See prime factorization and detailed working.
4. Reset or Recalculate: Try new sets of numbers easily.

Features of the Digital Calculator LCM & HCF Calculator

We built this tool to make every mathematical task easier from quick checks to detailed study support.

Key Features:

• Calculates LCM and HCF simultaneously.
• Handles multiple numbers (2 to 10 or more).
• Supports large values and decimals.
• Displays step-by-step prime factorization.
• Instant and accurate results.
• Mobile-friendly design use it anytime, anywhere.
• Completely free and ad-free.

Try the LCM & HCF Calculator at Digital Calculator now and get instant results with one click.

Table of Common LCM and HCF Values

HCF and LCM of Fractions

HCF of Fractions:

HCF = HCF of Numerators / LCM of Denominators

Example: Find HCF of 1/2, 2/3

HCF (numerators) = 1

LCM (denominators) = 6

Result = 1/6

LCM of Fractions:

LCM = LCM of Numerators / HCF of Denominators

Example: Find LCM of 1/2, 2/3

LCM (numerators) = 2

HCF (denominators) = 1

Result = 2/1 = 2

Tips for Finding LCM and HCF

1. Start small: Use smaller primes (2, 3, 5, 7) when factorizing.
    
2. Use the product relation: LCM × HCF = a × b (saves time).
    
3. Convert decimals: Multiply all by powers of 10 before finding factors.
    
4. For multiple numbers: Calculate HCF/LCM pairwise.
   Example: HCF(8, 12, 20) = HCF(HCF(8, 12), 20).

Real-World Examples