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 - Page 13: 87


A greatest common factor (GCF) is the number that divides into a group of two or more numbers to get a whole number. The least common multiple (LCM) is the smallest positive number that is a multiple of a group of two or more numbers.

Work Step by Step

The GCF can be found by listing all of the primes factors of all of the numbers in the group and then multiplying the factors that all of the numbers have in common. If there aren't any prime factors that the numbers have in common, then the greatest common factor is one. The LCM can be found by listing the multiples of each number from the set of two or more numbers. You continue listing the multiples until you find a number that all of the numbers in the set have. The first multiple you find will be the LCM since it is the smallest. It is impossible to find the Greatest Common Multiple since numbers go to infinity.
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