Q:

What is the LCM of 144 and 34?

Accepted Solution

A:
Solution: The LCM of 144 and 34 is 2448 Methods How to find the LCM of 144 and 34 using Prime Factorization One way to find the LCM of 144 and 34 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 34? 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 34: 2 1 × 1 7 1 2^1 × 17^1 2 1 × 1 7 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, 17 2 4 × 3 2 × 1 7 1 = 2448 2^4 × 3^2 × 17^1 = 2448 2 4 × 3 2 × 1 7 1 = 2448 Through this we see that the LCM of 144 and 34 is 2448. How to Find the LCM of 144 and 34 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 144 and 34 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 34: What are the Multiples of 144? What are the Multiples of 34? Let’s take a look at the first 10 multiples for each of these numbers, 144 and 34: First 10 Multiples of 144: 144, 288, 432, 576, 720, 864, 1008, 1152, 1296, 1440 First 10 Multiples of 34: 34, 68, 102, 136, 170, 204, 238, 272, 306, 340 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 34 are 2448, 4896, 7344. Because 2448 is the smallest, it is the least common multiple. The LCM of 144 and 34 is 2448. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 2 and 77? What is the LCM of 93 and 35? What is the LCM of 124 and 24? What is the LCM of 66 and 63? What is the LCM of 146 and 126?