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GCF and LCM Calculator

Find the Greatest Common Factor (GCF/GCD) and Least Common Multiple (LCM) of two integers.

Greatest Common Factor (GCF / GCD)
12

Highest integer dividing both 48 and 180

Least Common Multiple (LCM)
720

Smallest integer multiple of both 48 and 180

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Calculation Guide & Reference

GCF (Greatest Common Factor) & LCM Mathematics

GCF and LCM calculator finds the Greatest Common Factor and Least Common Multiple of two integers using the Euclidean algorithm.

Standardized Mathematical Formula
GCF via Euclidean algorithm | LCM = |A × B| / GCF

The Euclidean algorithm finds the GCF by repeatedly replacing the larger number with the remainder of dividing it by the smaller, until the remainder is zero. The LCM is then derived directly from the GCF.

Variables:
A:First integer
B:Second integer
How It Works (Step-by-Step)
  • 1Enter two integers.
  • 2View their Greatest Common Factor (GCF/GCD) and Least Common Multiple (LCM).
Real-World Numerical Example
GCF and LCM of 48 and 180

Find the GCF and LCM of 48 and 180.

•Euclidean algorithm: gcd(48,180) → gcd(180 mod 48=36, 48) → gcd(48 mod 36=12, 36) → gcd(36 mod 12=0) → GCF = 12.
•LCM = (48 × 180) / 12 = 8,640 / 12 = 720.
Result: The GCF of 48 and 180 is 12; the LCM is 720.
Calculation Best Practices & Tips
Examine the discriminant (b² - 4ac) before solving quadratics to instantly know if roots are real, distinct, repeated, or complex.
In statistical analysis, always check both the mean and median to identify if data distribution is skewed by outliers.
When calculating percentage changes, ensure you divide by the original starting baseline value: ((New - Old) / Old) * 100.

Frequently Asked Questions (FAQ)

The fastest method is the Euclidean algorithm: repeatedly replace the larger number with the remainder of dividing it by the smaller number, until the remainder reaches zero — the last nonzero remainder is the GCF.

Once you know the GCF, LCM = (A × B) / GCF — for 48 and 180 with a GCF of 12, LCM = (48 × 180) / 12 = 720.

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