How to Find GCD and LCM
The Greatest Common Divisor (GCD) is the largest positive integer that divides two numbers without a remainder. The Least Common Multiple (LCM) is the smallest positive integer that is divisible by both numbers. These concepts are fundamental to simplifying fractions, solving problems involving periodic events, and scheduling tasks that repeat at different intervals.
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Formula
GCD & LCM Calculator
Find the Greatest Common Divisor and Least Common Multiple of two integers.
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Worked Example
Given:
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FAQs
How is GCD used to simplify fractions?
To simplify a fraction, divide both numerator and denominator by their GCD. For example, 48/18: GCD(48,18) = 6, so 48/18 = (48÷6)/(18÷6) = 8/3. The fraction is now in its simplest form.
What is a real-world use of LCM?
LCM solves problems involving cycles that repeat at different intervals. For example, if two buses run every 12 and 18 minutes respectively, they will both be at the stop at the same time every LCM(12,18) = 36 minutes. LCM also finds the lowest common denominator for adding fractions.
What is the Euclidean algorithm?
The Euclidean algorithm efficiently computes GCD by repeated division: GCD(a,b) = GCD(b, a mod b), repeating until the remainder is zero. For GCD(48,18): GCD(48,18) → GCD(18,12) → GCD(12,6) → GCD(6,0) = 6. It is one of the oldest algorithms known, dating to ancient Greece.