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LCM & GCD Calculator

Find Least Common Multiple (LCM) and Greatest Common Divisor (GCD / HCF)

LCM (Least Common Multiple)
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GCD / HCF (Greatest Common Divisor)
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Numbers entered—
LCM—
GCD / HCF—
LCM × GCD—
Are all co-prime?—
Prime Factorization
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What is LCM & GCD Calculator?

Free LCM and GCD (HCF) calculator. Find Least Common Multiple and Greatest Common Divisor of multiple numbers with step-by-step solution. Fast, accurate mathematical calculators that show step-by-step working. TekPulse's LCM & GCD Calculator is completely free — no signup, no ads in results, and no data stored on our servers.

How to Use LCM & GCD Calculator Online

  1. Enter two or more numbers separated by commas
  2. Click Calculate to get the LCM (Least Common Multiple) and GCD (Greatest Common Divisor)
  3. The step-by-step working using the Euclidean algorithm is shown below the result
  4. Use LCM to find common denominators for fractions; use GCD to simplify fractions
  5. Enter up to 10 numbers to find their collective LCM and GCD

LCM & GCD Calculator Formula & Calculation

GCD(a,b) via Euclidean algorithm (repeated remainder) | LCM(a,b) = |a × b| ÷ GCD(a,b)

The Euclidean algorithm computes GCD by repeatedly replacing the pair (a, b) with (b, a mod b) until the remainder is zero — the last non-zero value is the GCD. For more than two numbers, GCD and LCM are computed pairwise/cumulatively across the list. LCM is then derived from the identity that the product of two numbers equals the product of their GCD and LCM. The tool also shows the prime factorization of each number as a cross-check.

Example: GCD(48, 180): 180 mod 48 = 36 → 48 mod 36 = 12 → 36 mod 12 = 0 → GCD = 12. LCM(48,180) = (48 × 180) ÷ 12 = 720.

Key Factors That Affect Your Result

  1. Multiple numbers — For 3 or more numbers, GCD and LCM are computed by reducing the list pairwise (GCD(GCD(a,b),c), and similarly for LCM) — the result is mathematically the same regardless of the order numbers are combined.
  2. Prime factorization cross-check — The tool additionally decomposes each number into prime factors (e.g., 180 = 2² × 3² × 5), which is an alternative, slower method of finding GCD/LCM but useful for verifying or understanding the result.
  3. Use cases — GCD is used to simplify fractions and ratios; LCM is used for problems like finding a common cycle time or aligning repeating events (e.g., "two buses leave every 12 and 18 minutes — when do they next leave together?" → LCM(12,18) = 36 minutes).

Why Use TekPulse LCM & GCD Calculator?

Runs Entirely in Your Browser
LCM and GCD are calculated instantly with JavaScript — no data is uploaded
Multiple Numbers at Once
Finds the LCM and GCD/HCF of two or more numbers in a single calculation, not just pairs
Prime Factorization Shown
Displays the prime factorization of each number used to derive the result
Co-Prime Check
Indicates whether the entered numbers are co-prime (GCD = 1)

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Frequently Asked Questions

GCD (Greatest Common Divisor), also called HCF (Highest Common Factor), is the largest number that divides all given numbers without remainder. GCD(12, 18) = 6.

LCM (Least Common Multiple) is the smallest number that is a multiple of all given numbers. LCM(4, 6) = 12. Used in adding fractions and scheduling problems.

For two numbers a and b: LCM(a,b) × GCD(a,b) = a × b. Example: LCM(4,6) = 12, GCD(4,6) = 2. Check: 12 × 2 = 24 = 4 × 6 ✓

Divide the larger number by the smaller. Replace the larger with the smaller and the smaller with the remainder. Repeat until remainder is 0. The last non-zero remainder is the GCD. Example: GCD(48,18): 48=18×2+12, 18=12×1+6, 12=6×2+0 → GCD=6.

GCD is used to simplify fractions (divide numerator and denominator by GCD), solve Diophantine equations, check if two numbers are coprime (GCD=1), and in cryptography (RSA algorithm uses coprime numbers).

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