Q:

What is the LCM of 104 and 142?

Accepted Solution

A:
Solution: The LCM of 104 and 142 is 7384 Methods How to find the LCM of 104 and 142 using Prime Factorization One way to find the LCM of 104 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 104? What are the Factors of 142? Here is the prime factorization of 104: 2 3 × 1 3 1 2^3 × 13^1 2 3 × 1 3 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: 2, 13, 71 2 3 × 1 3 1 × 7 1 1 = 7384 2^3 × 13^1 × 71^1 = 7384 2 3 × 1 3 1 × 7 1 1 = 7384 Through this we see that the LCM of 104 and 142 is 7384. How to Find the LCM of 104 and 142 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 104 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, 104 and 142: What are the Multiples of 104? What are the Multiples of 142? Let’s take a look at the first 10 multiples for each of these numbers, 104 and 142: First 10 Multiples of 104: 104, 208, 312, 416, 520, 624, 728, 832, 936, 1040 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 104 and 142 are 7384, 14768, 22152. Because 7384 is the smallest, it is the least common multiple. The LCM of 104 and 142 is 7384. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 99 and 29? What is the LCM of 145 and 141? What is the LCM of 98 and 54? What is the LCM of 126 and 37? What is the LCM of 1 and 36?