Calculate GCD and LCM with step-by-step solutions
GCD and LCM Calculator
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GCD Result
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GCD Calculation Method
The Greatest Common Divisor (GCD) is calculated using the Euclidean Algorithm:
Example: GCD of 56 and 98
1. Divide 98 by 56 → 98 ÷ 56 = 1 remainder 42
2. Replace 98 with 56 and 56 with 42 → GCD(56, 42)
3. Divide 56 by 42 → 56 ÷ 42 = 1 remainder 14
4. Replace 56 with 42 and 42 with 14 → GCD(42, 14)
5. Divide 42 by 14 → 42 ÷ 14 = 3 remainder 0
6. GCD is 14 when remainder becomes 0
2. Replace 98 with 56 and 56 with 42 → GCD(56, 42)
3. Divide 56 by 42 → 56 ÷ 42 = 1 remainder 14
4. Replace 56 with 42 and 42 with 14 → GCD(42, 14)
5. Divide 42 by 14 → 42 ÷ 14 = 3 remainder 0
6. GCD is 14 when remainder becomes 0
LCM Calculation Method
The Least Common Multiple (LCM) is calculated using the formula:
LCM(a, b) = (a × b) / GCD(a, b)
LCM(a, b) = (a × b) / GCD(a, b)
Example: LCM of 12 and 18
1. GCD of 12 and 18 is 6
2. Multiply numbers: 12 × 18 = 216
3. Divide by GCD: 216 ÷ 6 = 36
4. LCM is 36
2. Multiply numbers: 12 × 18 = 216
3. Divide by GCD: 216 ÷ 6 = 36
4. LCM is 36
About GCD and LCM
What is GCD?
The Greatest Common Divisor (GCD) of two numbers is the largest positive integer that divides both numbers without leaving a remainder.
Also known as the Greatest Common Factor (GCF) or Highest Common Factor (HCF).
Also known as the Greatest Common Factor (GCF) or Highest Common Factor (HCF).
What is LCM?
The Least Common Multiple (LCM) of two numbers is the smallest positive integer that is divisible by both numbers.
LCM is particularly useful for finding common denominators in fractions.
LCM is particularly useful for finding common denominators in fractions.
Real-World Applications
GCD Applications:
- Simplifying fractions to their lowest terms
- Distributing items equally into groups
- Cryptography algorithms
- Engineering calculations for gear ratios
- Finding common denominators when adding fractions
- Scheduling repeating events
- Determining when astronomical events will coincide
- Manufacturing production cycles
Historical Background
The Euclidean algorithm for finding GCD is one of the oldest algorithms still in common use. It was described by the Greek mathematician Euclid around 300 BC in his work “Elements”.
The concept of LCM has been used since ancient times for astronomical calculations and calendar systems.
The concept of LCM has been used since ancient times for astronomical calculations and calendar systems.
Why Use Our GCD and LCM Calculator?
Detailed Steps
See exactly how calculations are performed with step-by-step explanations.
Fast & Accurate
Get instant results using optimized algorithms for GCD and LCM calculations.
Educational
Perfect for students learning number theory and algebra concepts.
Handles Large Numbers
Calculates GCD and LCM for very large integers efficiently.
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