Q:

What is the LCM of 128 and 123?

Accepted Solution

A:
Solution: The LCM of 128 and 123 is 15744 Methods How to find the LCM of 128 and 123 using Prime Factorization One way to find the LCM of 128 and 123 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 128? What are the Factors of 123? Here is the prime factorization of 128: 2 7 2^7 2 7 And this is the prime factorization of 123: 3 1 × 4 1 1 3^1 × 41^1 3 1 × 4 1 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, 41 2 7 × 3 1 × 4 1 1 = 15744 2^7 × 3^1 × 41^1 = 15744 2 7 × 3 1 × 4 1 1 = 15744 Through this we see that the LCM of 128 and 123 is 15744. How to Find the LCM of 128 and 123 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 128 and 123 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, 128 and 123: What are the Multiples of 128? What are the Multiples of 123? Let’s take a look at the first 10 multiples for each of these numbers, 128 and 123: First 10 Multiples of 128: 128, 256, 384, 512, 640, 768, 896, 1024, 1152, 1280 First 10 Multiples of 123: 123, 246, 369, 492, 615, 738, 861, 984, 1107, 1230 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 128 and 123 are 15744, 31488, 47232. Because 15744 is the smallest, it is the least common multiple. The LCM of 128 and 123 is 15744. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 61 and 4? What is the LCM of 130 and 39? What is the LCM of 141 and 125? What is the LCM of 70 and 54? What is the LCM of 120 and 36?