## Elementary Algebra

Published by Cengage Learning

# Chapter 1 - Some Basic Concepts of Arithmetic and Algebra - 1.2 - Prime and Composite Numbers - Problem Set 1.2 - Page 13: 76

#### Answer

$24$

#### Work Step by Step

Factor each number completely to obtain: $8= 2\cdot 2 \cdot 2 \\12 = 2 \cdot 2 \cdot 3$ The different factors that appear in the prime factorization of the given numbers are 2 and 3. The maximum number of times that each unique factor appears in the factorization is: For 2: three times For 3: once The least common multiple will have three 2s and one 3. Thus, the least common multiple of the given numbers is: $=2\cdot 2 \cdot 2 \cdot 3 \\= 24$

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