Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 5 - Number Theory and the Real Number System - Chapter Summary, Review, and Test - Review Exercises: 7

Answer

greatest common divisor = 6 least common multiple = 900

Work Step by Step

Factor each number completely to find: $36 = 6(6) = 2(3)(2)(3)=2(2)(3)(3) \\150 = 25(6) = 5(5)(2)(3) = 2(3)(5)(5)$ Greatest Common Divisor (GCD): Note that the common factors to both numbers are: 2 (once) 3 (once) Thus, the GCD of the two numbers is: GCD =$2(3) = 6$ Least Common Multiple (LCM): Take note of the maximum number of times that each unique factor appears in the factorization of the two given numbers: 2 - two times 3 - two times 5 - two times Thus, the LCM of the two given numbers is: LCM = $2(2)(3)(3)(5)(5) = 900$
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