Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter R - Section R.1 - Factors and the Least Common Multiple - Exercise Set - Page R-7: 61

Answer

$35$ nights

Work Step by Step

To find out how often Craig Campanella and Edie Hall will have the same night off, we need to determine the least common multiple ($LCM$) of $5$ and $7$. The $LCM$ will represent the number of nights after which their schedules will align. The prime factorization of $5$ is simply $5$, as it is a prime number. The prime factorization of $7$ is also $7$, as it is also a prime number. To find the $LCM$, we take the highest power of each prime factor: $LCM(5, 7) = 5 \cdot 7 = 35$. It could be concluded that Craig and Edie will have the same night off every $35$ nights.
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