Q:

What is the LCM of 133 and 144?

Accepted Solution

A:
Solution: The LCM of 133 and 144 is 19152 Methods How to find the LCM of 133 and 144 using Prime Factorization One way to find the LCM of 133 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 133? What are the Factors of 144? Here is the prime factorization of 133: 7 1 × 1 9 1 7^1 × 19^1 7 1 × 1 9 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: 7, 19, 2, 3 2 4 × 3 2 × 7 1 × 1 9 1 = 19152 2^4 × 3^2 × 7^1 × 19^1 = 19152 2 4 × 3 2 × 7 1 × 1 9 1 = 19152 Through this we see that the LCM of 133 and 144 is 19152. How to Find the LCM of 133 and 144 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 133 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, 133 and 144: What are the Multiples of 133? What are the Multiples of 144? Let’s take a look at the first 10 multiples for each of these numbers, 133 and 144: First 10 Multiples of 133: 133, 266, 399, 532, 665, 798, 931, 1064, 1197, 1330 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 133 and 144 are 19152, 38304, 57456. Because 19152 is the smallest, it is the least common multiple. The LCM of 133 and 144 is 19152. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 147 and 58? What is the LCM of 67 and 88? What is the LCM of 77 and 65? What is the LCM of 25 and 22? What is the LCM of 44 and 138?