Q:

What is the LCM of 106 and 69?

Accepted Solution

A:
Solution: The LCM of 106 and 69 is 7314 Methods How to find the LCM of 106 and 69 using Prime Factorization One way to find the LCM of 106 and 69 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 69? 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 69: 3 1 × 2 3 1 3^1 × 23^1 3 1 × 2 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, 23 2 1 × 3 1 × 2 3 1 × 5 3 1 = 7314 2^1 × 3^1 × 23^1 × 53^1 = 7314 2 1 × 3 1 × 2 3 1 × 5 3 1 = 7314 Through this we see that the LCM of 106 and 69 is 7314. How to Find the LCM of 106 and 69 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 106 and 69 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 69: What are the Multiples of 106? What are the Multiples of 69? Let’s take a look at the first 10 multiples for each of these numbers, 106 and 69: First 10 Multiples of 106: 106, 212, 318, 424, 530, 636, 742, 848, 954, 1060 First 10 Multiples of 69: 69, 138, 207, 276, 345, 414, 483, 552, 621, 690 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 69 are 7314, 14628, 21942. Because 7314 is the smallest, it is the least common multiple. The LCM of 106 and 69 is 7314. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 145 and 112? What is the LCM of 97 and 84? What is the LCM of 86 and 77? What is the LCM of 27 and 58? What is the LCM of 70 and 65?