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Proposition: Relationship Between the Greatest Common Divisor and the Least Common Multiple

Let \(a > 0\), \(b > 0\) are natural numbers. Then the least common multiple \(\operatorname{lcm}(a,b)\) and the greatest common divisor \(\operatorname{gcd}(a,b)\) are related with each other as follows: \[\operatorname{lcm}(a,b)\cdot \operatorname{gcd}(a,b)=a\cdot b.\]

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Proofs: 1

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Proofs: 1 2

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References

Bibliography

1. Landau, Edmund: "Vorlesungen über Zahlentheorie, Aus der Elementaren Zahlentheorie", S. Hirzel, Leipzig, 1927