GCD & LCM Calculator
Find the Greatest Common Divisor (GCD) and Least Common Multiple (LCM) of two integers.
Greatest Common Divisor (GCD)
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How to Compute GCD and LCM
- Enter two or more positive integers.
- The tool computes the Greatest Common Divisor (GCD) using the Euclidean algorithm.
- The Least Common Multiple (LCM) is derived simultaneously via
LCM(a, b) = |a × b| / GCD(a, b).
Euclidean Algorithm & Relationship
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GCD (Euclid):
GCD(a, b) = GCD(b, a mod b)until remainder is 0. -
LCM Identity:
LCM(a, b) = (|a × b|) / GCD(a, b).
Worked Numerical Solutions
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For numbers 24 and 36:
GCD = 12,LCM = 72. -
For numbers 15 and 25:
GCD = 5,LCM = 75.
Common Applications
- Finding common denominators for complex fraction sums.
- Synchronizing cyclic events and gear tooth mesh patterns.
- Splitting items evenly into identical party bags or shipping packages.
Frequently Asked Questions
Can this tool calculate GCD for more than two numbers?
Yes. It applies associative reduction: <code>GCD(a, b, c) = GCD(GCD(a, b), c)</code>.
What if the GCD is 1?
When GCD(a, b) = 1, the numbers are coprime (mutually prime).