Q:

What is the LCM of 105 and 142?

Accepted Solution

A:
Solution: The LCM of 105 and 142 is 14910 Methods How to find the LCM of 105 and 142 using Prime Factorization One way to find the LCM of 105 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 105? What are the Factors of 142? Here is the prime factorization of 105: 3 1 × 5 1 × 7 1 3^1 × 5^1 × 7^1 3 1 × 5 1 × 7 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: 3, 5, 7, 2, 71 2 1 × 3 1 × 5 1 × 7 1 × 7 1 1 = 14910 2^1 × 3^1 × 5^1 × 7^1 × 71^1 = 14910 2 1 × 3 1 × 5 1 × 7 1 × 7 1 1 = 14910 Through this we see that the LCM of 105 and 142 is 14910. How to Find the LCM of 105 and 142 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 105 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, 105 and 142: What are the Multiples of 105? What are the Multiples of 142? Let’s take a look at the first 10 multiples for each of these numbers, 105 and 142: First 10 Multiples of 105: 105, 210, 315, 420, 525, 630, 735, 840, 945, 1050 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 105 and 142 are 14910, 29820, 44730. Because 14910 is the smallest, it is the least common multiple. The LCM of 105 and 142 is 14910. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 19 and 13? What is the LCM of 21 and 81? What is the LCM of 107 and 139? What is the LCM of 4 and 89? What is the LCM of 43 and 108?