Q:

What is the LCM of 143 and 40?

Accepted Solution

A:
Solution: The LCM of 143 and 40 is 5720 Methods How to find the LCM of 143 and 40 using Prime Factorization One way to find the LCM of 143 and 40 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 40? 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 40: 2 3 × 5 1 2^3 × 5^1 2 3 × 5 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, 5 2 3 × 5 1 × 1 1 1 × 1 3 1 = 5720 2^3 × 5^1 × 11^1 × 13^1 = 5720 2 3 × 5 1 × 1 1 1 × 1 3 1 = 5720 Through this we see that the LCM of 143 and 40 is 5720. How to Find the LCM of 143 and 40 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 143 and 40 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 40: What are the Multiples of 143? What are the Multiples of 40? Let’s take a look at the first 10 multiples for each of these numbers, 143 and 40: First 10 Multiples of 143: 143, 286, 429, 572, 715, 858, 1001, 1144, 1287, 1430 First 10 Multiples of 40: 40, 80, 120, 160, 200, 240, 280, 320, 360, 400 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 40 are 5720, 11440, 17160. Because 5720 is the smallest, it is the least common multiple. The LCM of 143 and 40 is 5720. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 134 and 43? What is the LCM of 87 and 35? What is the LCM of 91 and 79? What is the LCM of 17 and 93? What is the LCM of 122 and 42?