Q:

What is the LCM of 143 and 82?

Accepted Solution

A:
Solution: The LCM of 143 and 82 is 11726 Methods How to find the LCM of 143 and 82 using Prime Factorization One way to find the LCM of 143 and 82 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 143? What are the Factors of 82? Here is the prime factorization of 143: 1 1 1 × 1 3 1 11^1 × 13^1 1 1 1 × 1 3 1 And this is the prime factorization of 82: 2 1 × 4 1 1 2^1 × 41^1 2 1 × 4 1 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: 11, 13, 2, 41 2 1 × 1 1 1 × 1 3 1 × 4 1 1 = 11726 2^1 × 11^1 × 13^1 × 41^1 = 11726 2 1 × 1 1 1 × 1 3 1 × 4 1 1 = 11726 Through this we see that the LCM of 143 and 82 is 11726. How to Find the LCM of 143 and 82 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 143 and 82 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, 143 and 82: What are the Multiples of 143? What are the Multiples of 82? Let’s take a look at the first 10 multiples for each of these numbers, 143 and 82: First 10 Multiples of 143: 143, 286, 429, 572, 715, 858, 1001, 1144, 1287, 1430 First 10 Multiples of 82: 82, 164, 246, 328, 410, 492, 574, 656, 738, 820 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 143 and 82 are 11726, 23452, 35178. Because 11726 is the smallest, it is the least common multiple. The LCM of 143 and 82 is 11726. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 34 and 23? What is the LCM of 60 and 128? What is the LCM of 45 and 120? What is the LCM of 65 and 66? What is the LCM of 73 and 26?