Q:

What is the LCM of 123 and 8?

Accepted Solution

A:
Solution: The LCM of 123 and 8 is 984 Methods How to find the LCM of 123 and 8 using Prime Factorization One way to find the LCM of 123 and 8 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 123? What are the Factors of 8? Here is the prime factorization of 123: 3 1 × 4 1 1 3^1 × 41^1 3 1 × 4 1 1 And this is the prime factorization of 8: 2 3 2^3 2 3 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: 3, 41, 2 2 3 × 3 1 × 4 1 1 = 984 2^3 × 3^1 × 41^1 = 984 2 3 × 3 1 × 4 1 1 = 984 Through this we see that the LCM of 123 and 8 is 984. How to Find the LCM of 123 and 8 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 123 and 8 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, 123 and 8: What are the Multiples of 123? What are the Multiples of 8? Let’s take a look at the first 10 multiples for each of these numbers, 123 and 8: First 10 Multiples of 123: 123, 246, 369, 492, 615, 738, 861, 984, 1107, 1230 First 10 Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80 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 123 and 8 are 984, 1968, 2952. Because 984 is the smallest, it is the least common multiple. The LCM of 123 and 8 is 984. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 20 and 21? What is the LCM of 50 and 116? What is the LCM of 68 and 46? What is the LCM of 118 and 86? What is the LCM of 17 and 79?