Q:

What is the LCM of 19 and 124?

Accepted Solution

A:
Solution: The LCM of 19 and 124 is 2356 Methods How to find the LCM of 19 and 124 using Prime Factorization One way to find the LCM of 19 and 124 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 19? What are the Factors of 124? Here is the prime factorization of 19: 1 9 1 19^1 1 9 1 And this is the prime factorization of 124: 2 2 × 3 1 1 2^2 × 31^1 2 2 × 3 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: 19, 2, 31 2 2 × 1 9 1 × 3 1 1 = 2356 2^2 × 19^1 × 31^1 = 2356 2 2 × 1 9 1 × 3 1 1 = 2356 Through this we see that the LCM of 19 and 124 is 2356. How to Find the LCM of 19 and 124 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 19 and 124 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, 19 and 124: What are the Multiples of 19? What are the Multiples of 124? Let’s take a look at the first 10 multiples for each of these numbers, 19 and 124: First 10 Multiples of 19: 19, 38, 57, 76, 95, 114, 133, 152, 171, 190 First 10 Multiples of 124: 124, 248, 372, 496, 620, 744, 868, 992, 1116, 1240 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 19 and 124 are 2356, 4712, 7068. Because 2356 is the smallest, it is the least common multiple. The LCM of 19 and 124 is 2356. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 141 and 109? What is the LCM of 90 and 126? What is the LCM of 91 and 146? What is the LCM of 145 and 95? What is the LCM of 74 and 121?