Q:

What is the LCM of 19 and 142?

Accepted Solution

A:
Solution: The LCM of 19 and 142 is 2698 Methods How to find the LCM of 19 and 142 using Prime Factorization One way to find the LCM of 19 and 142 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 142? Here is the prime factorization of 19: 1 9 1 19^1 1 9 1 And this is the prime factorization of 142: 2 1 × 7 1 1 2^1 × 71^1 2 1 × 7 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, 71 2 1 × 1 9 1 × 7 1 1 = 2698 2^1 × 19^1 × 71^1 = 2698 2 1 × 1 9 1 × 7 1 1 = 2698 Through this we see that the LCM of 19 and 142 is 2698. How to Find the LCM of 19 and 142 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 19 and 142 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 142: What are the Multiples of 19? What are the Multiples of 142? Let’s take a look at the first 10 multiples for each of these numbers, 19 and 142: First 10 Multiples of 19: 19, 38, 57, 76, 95, 114, 133, 152, 171, 190 First 10 Multiples of 142: 142, 284, 426, 568, 710, 852, 994, 1136, 1278, 1420 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 142 are 2698, 5396, 8094. Because 2698 is the smallest, it is the least common multiple. The LCM of 19 and 142 is 2698. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 147 and 90? What is the LCM of 38 and 60? What is the LCM of 76 and 29? What is the LCM of 30 and 1? What is the LCM of 34 and 111?