Q:

What is the LCM of 106 and 129?

Accepted Solution

A:
Solution: The LCM of 106 and 129 is 13674 Methods How to find the LCM of 106 and 129 using Prime Factorization One way to find the LCM of 106 and 129 is to start by comparing the prime factorization of each number. To find the prime factorization, you can follow the instructions for each number here: What are the Factors of 106? What are the Factors of 129? Here is the prime factorization of 106: 2 1 × 5 3 1 2^1 × 53^1 2 1 × 5 3 1 And this is the prime factorization of 129: 3 1 × 4 3 1 3^1 × 43^1 3 1 × 4 3 1 When you compare the prime factorization of these two numbers, you want to look for the highest power that each prime factor is raised to. In this case, there are these prime factors to consider: 2, 53, 3, 43 2 1 × 3 1 × 4 3 1 × 5 3 1 = 13674 2^1 × 3^1 × 43^1 × 53^1 = 13674 2 1 × 3 1 × 4 3 1 × 5 3 1 = 13674 Through this we see that the LCM of 106 and 129 is 13674. How to Find the LCM of 106 and 129 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 106 and 129 is to begin to list a few multiples for each number. If you need a refresher on how to find the multiples of these numbers, you can see the walkthroughs in the links below for each number. Let’s take a look at the multiples for each of these numbers, 106 and 129: What are the Multiples of 106? What are the Multiples of 129? Let’s take a look at the first 10 multiples for each of these numbers, 106 and 129: First 10 Multiples of 106: 106, 212, 318, 424, 530, 636, 742, 848, 954, 1060 First 10 Multiples of 129: 129, 258, 387, 516, 645, 774, 903, 1032, 1161, 1290 You can continue to list out the multiples of these numbers as long as needed to find a match. Once you do find a match, or several matches, the smallest of these matches would be the Least Common Multiple. For instance, the first matching multiple(s) of 106 and 129 are 13674, 27348, 41022. Because 13674 is the smallest, it is the least common multiple. The LCM of 106 and 129 is 13674. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 113 and 60? What is the LCM of 101 and 76? What is the LCM of 94 and 17? What is the LCM of 74 and 73? What is the LCM of 120 and 93?