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Math / Discrete Mathematics with Applications 4 / Chapter 4.8 / Problem 28E

Discrete Mathematics with Applications | 4th Edition | ISBN: 9780495391326 | Authors: Susanna S. Epp

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Chapter 4, Problem 28E

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QUESTION: Exercises 25–29 refer to the following definition.Prove that for all integers a and b, gcd(a, b) | lcm(a, b).

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QUESTION: Exercises 25–29 refer to the following definition.Prove that for all integers a and b, gcd(a, b) | lcm(a, b).

ANSWER:

Solution :

Here, we need to prove that for all integers a and b, gcd(a, b) | lcm(a, b).

Step 1. Let gcd(a,b) = d then $d\ |\ a\ and\ d\ |b\ \Rightarrow{}d\ |\ ab$ ………….(1)

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