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: 91



Work Step by Step

We are trying to find a number $n$ such that division by $2$, $3$, $4$, $5$, or $6$ leaves a remainder of $1$. The solution to this problem is $1$ greater than the LCM of these numbers because adding $1$ to the LCM provides a number that leaves a remainder of $1$ when divided by the list above. The least common multiple of 2, 3, 4, 5, and 6 is the lowest number that is a multiple of these numbers, which is 60. Thus, we obtain: $=60+1=61$.
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