Q:

What is the LCM of 126 and 143?

Accepted Solution

A:
Solution: The LCM of 126 and 143 is 18018 Methods How to find the LCM of 126 and 143 using Prime Factorization One way to find the LCM of 126 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 126? What are the Factors of 143? Here is the prime factorization of 126: 2 1 × 3 2 × 7 1 2^1 × 3^2 × 7^1 2 1 × 3 2 × 7 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: 2, 3, 7, 11, 13 2 1 × 3 2 × 7 1 × 1 1 1 × 1 3 1 = 18018 2^1 × 3^2 × 7^1 × 11^1 × 13^1 = 18018 2 1 × 3 2 × 7 1 × 1 1 1 × 1 3 1 = 18018 Through this we see that the LCM of 126 and 143 is 18018. How to Find the LCM of 126 and 143 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 126 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, 126 and 143: What are the Multiples of 126? What are the Multiples of 143? Let’s take a look at the first 10 multiples for each of these numbers, 126 and 143: First 10 Multiples of 126: 126, 252, 378, 504, 630, 756, 882, 1008, 1134, 1260 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 126 and 143 are 18018, 36036, 54054. Because 18018 is the smallest, it is the least common multiple. The LCM of 126 and 143 is 18018. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 62 and 20? What is the LCM of 93 and 12? What is the LCM of 39 and 57? What is the LCM of 129 and 134? What is the LCM of 50 and 143?