Q:

What is the LCM of 106 and 133?

Accepted Solution

A:
Solution: The LCM of 106 and 133 is 14098 Methods How to find the LCM of 106 and 133 using Prime Factorization One way to find the LCM of 106 and 133 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 133? 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 133: 7 1 × 1 9 1 7^1 × 19^1 7 1 × 1 9 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, 7, 19 2 1 × 7 1 × 1 9 1 × 5 3 1 = 14098 2^1 × 7^1 × 19^1 × 53^1 = 14098 2 1 × 7 1 × 1 9 1 × 5 3 1 = 14098 Through this we see that the LCM of 106 and 133 is 14098. How to Find the LCM of 106 and 133 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 106 and 133 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 133: What are the Multiples of 106? What are the Multiples of 133? Let’s take a look at the first 10 multiples for each of these numbers, 106 and 133: First 10 Multiples of 106: 106, 212, 318, 424, 530, 636, 742, 848, 954, 1060 First 10 Multiples of 133: 133, 266, 399, 532, 665, 798, 931, 1064, 1197, 1330 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 133 are 14098, 28196, 42294. Because 14098 is the smallest, it is the least common multiple. The LCM of 106 and 133 is 14098. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 68 and 134? What is the LCM of 101 and 24? What is the LCM of 116 and 91? What is the LCM of 80 and 86? What is the LCM of 35 and 4?