Q:

What is the LCM of 142 and 144?

Accepted Solution

A:
Solution: The LCM of 142 and 144 is 10224 Methods How to find the LCM of 142 and 144 using Prime Factorization One way to find the LCM of 142 and 144 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 142? What are the Factors of 144? Here is the prime factorization of 142: 2 1 × 7 1 1 2^1 × 71^1 2 1 × 7 1 1 And this is the prime factorization of 144: 2 4 × 3 2 2^4 × 3^2 2 4 × 3 2 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, 71, 3 2 4 × 3 2 × 7 1 1 = 10224 2^4 × 3^2 × 71^1 = 10224 2 4 × 3 2 × 7 1 1 = 10224 Through this we see that the LCM of 142 and 144 is 10224. How to Find the LCM of 142 and 144 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 142 and 144 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, 142 and 144: What are the Multiples of 142? What are the Multiples of 144? Let’s take a look at the first 10 multiples for each of these numbers, 142 and 144: First 10 Multiples of 142: 142, 284, 426, 568, 710, 852, 994, 1136, 1278, 1420 First 10 Multiples of 144: 144, 288, 432, 576, 720, 864, 1008, 1152, 1296, 1440 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 142 and 144 are 10224, 20448, 30672. Because 10224 is the smallest, it is the least common multiple. The LCM of 142 and 144 is 10224. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 3 and 148? What is the LCM of 136 and 100? What is the LCM of 25 and 95? What is the LCM of 7 and 17? What is the LCM of 64 and 116?