Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 1 - Some Basic Concepts of Arithmetic and Algebra - 1.2 - Prime and Composite Numbers - Problem Set 1.2: 81

Answer

$392$

Work Step by Step

Factor each number completely to have: $49= 7 \cdot 7 \\56 = 2 \cdot 2 \cdot 2 \cdot 7$ The different factors that appear in the prime factorization of the given numbers are 2 and 7. The maximum number of times that each unique factor appears in the factorization is: For 2: three times For 7: two times The least common multiple will have three 2s and two 7s. Thus, the least common multiple of the given numbers is: $=2 \cdot 2\cdot 2 \cdot 7 \cdot 7 \\= 392$
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