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: 46

Answer

$90$

Work Step by Step

The least common multiple ($LCM$) of two numbers $a$ and $b$ is the smallest number which is a multiple of both numbers $a$ and $b$. We have to determine the $LCM$ of the numbers $18$ and $30$. First we write the prime factorization of each number: $18=2\cdot 3\cdot 3$ $30=2\cdot 3\cdot 5$ Then we take each factor the greatest number of times that it appears in any one prime factorization: $LCM=2\cdot 3\cdot 3\cdot 5 = 90$. The $LCM$ of the given numbers is $90$.
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