Q:

What is the LCM of 144 and 53?

Accepted Solution

A:
Solution: The LCM of 144 and 53 is 7632 Methods How to find the LCM of 144 and 53 using Prime Factorization One way to find the LCM of 144 and 53 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 144? What are the Factors of 53? Here is the prime factorization of 144: 2 4 × 3 2 2^4 × 3^2 2 4 × 3 2 And this is the prime factorization of 53: 5 3 1 53^1 5 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, 53 2 4 × 3 2 × 5 3 1 = 7632 2^4 × 3^2 × 53^1 = 7632 2 4 × 3 2 × 5 3 1 = 7632 Through this we see that the LCM of 144 and 53 is 7632. How to Find the LCM of 144 and 53 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 144 and 53 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, 144 and 53: What are the Multiples of 144? What are the Multiples of 53? Let’s take a look at the first 10 multiples for each of these numbers, 144 and 53: First 10 Multiples of 144: 144, 288, 432, 576, 720, 864, 1008, 1152, 1296, 1440 First 10 Multiples of 53: 53, 106, 159, 212, 265, 318, 371, 424, 477, 530 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 144 and 53 are 7632, 15264, 22896. Because 7632 is the smallest, it is the least common multiple. The LCM of 144 and 53 is 7632. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 13 and 2? What is the LCM of 137 and 49? What is the LCM of 148 and 149? What is the LCM of 143 and 67? What is the LCM of 112 and 18?