Q:

What is the LCM of 69 and 143?

Accepted Solution

A:
Solution: The LCM of 69 and 143 is 9867 Methods How to find the LCM of 69 and 143 using Prime Factorization One way to find the LCM of 69 and 143 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 69? What are the Factors of 143? Here is the prime factorization of 69: 3 1 × 2 3 1 3^1 × 23^1 3 1 × 2 3 1 And this is the prime factorization of 143: 1 1 1 × 1 3 1 11^1 × 13^1 1 1 1 × 1 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: 3, 23, 11, 13 3 1 × 1 1 1 × 1 3 1 × 2 3 1 = 9867 3^1 × 11^1 × 13^1 × 23^1 = 9867 3 1 × 1 1 1 × 1 3 1 × 2 3 1 = 9867 Through this we see that the LCM of 69 and 143 is 9867. How to Find the LCM of 69 and 143 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 69 and 143 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, 69 and 143: What are the Multiples of 69? What are the Multiples of 143? Let’s take a look at the first 10 multiples for each of these numbers, 69 and 143: First 10 Multiples of 69: 69, 138, 207, 276, 345, 414, 483, 552, 621, 690 First 10 Multiples of 143: 143, 286, 429, 572, 715, 858, 1001, 1144, 1287, 1430 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 69 and 143 are 9867, 19734, 29601. Because 9867 is the smallest, it is the least common multiple. The LCM of 69 and 143 is 9867. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 137 and 42? What is the LCM of 105 and 78? What is the LCM of 28 and 100? What is the LCM of 113 and 138? What is the LCM of 58 and 91?