Q:

What is the LCM of 124 and 39?

Accepted Solution

A:
Solution: The LCM of 124 and 39 is 4836 Methods How to find the LCM of 124 and 39 using Prime Factorization One way to find the LCM of 124 and 39 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 124? What are the Factors of 39? Here is the prime factorization of 124: 2 2 × 3 1 1 2^2 × 31^1 2 2 × 3 1 1 And this is the prime factorization of 39: 3 1 × 1 3 1 3^1 × 13^1 3 1 × 1 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, 31, 3, 13 2 2 × 3 1 × 1 3 1 × 3 1 1 = 4836 2^2 × 3^1 × 13^1 × 31^1 = 4836 2 2 × 3 1 × 1 3 1 × 3 1 1 = 4836 Through this we see that the LCM of 124 and 39 is 4836. How to Find the LCM of 124 and 39 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 124 and 39 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, 124 and 39: What are the Multiples of 124? What are the Multiples of 39? Let’s take a look at the first 10 multiples for each of these numbers, 124 and 39: First 10 Multiples of 124: 124, 248, 372, 496, 620, 744, 868, 992, 1116, 1240 First 10 Multiples of 39: 39, 78, 117, 156, 195, 234, 273, 312, 351, 390 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 124 and 39 are 4836, 9672, 14508. Because 4836 is the smallest, it is the least common multiple. The LCM of 124 and 39 is 4836. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 39 and 61? What is the LCM of 100 and 86? What is the LCM of 143 and 34? What is the LCM of 118 and 29? What is the LCM of 106 and 149?