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: 60

Answer

$LCM (a,b)=a\cdot b$ when $a$ and $b$ are relatively prime

Work Step by Step

When two numbers are relatively prime, their prime factorizations consist of distinct prime factors. Since there are no common factors between them, the $LCM$ is equals to their product. For example, in the case of $6$ and $7$, the prime factorization of $6$ is $2\cdot 3$, and the prime factorization of $7$ is $7$. Since $6$ and $7$ have no common prime factors, their $LCM$ is equal to their product: $6\cdot 7 = 42$. In general, if two numbers $A$ and $B$ are relatively prime, their $LCM$ is given by: $LCM(A, B) = A \cdot B$ This is because the $LCM$ is the smallest positive integer that is divisible by both $A$ and $B$, and when there are no common factors, the smallest integer that satisfies this condition is their product.
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