Q:

What is the LCM of 142 and 17?

Accepted Solution

A:
Solution: The LCM of 142 and 17 is 2414 Methods How to find the LCM of 142 and 17 using Prime Factorization One way to find the LCM of 142 and 17 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 142? What are the Factors of 17? Here is the prime factorization of 142: 2 1 × 7 1 1 2^1 × 71^1 2 1 × 7 1 1 And this is the prime factorization of 17: 1 7 1 17^1 1 7 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, 71, 17 2 1 × 1 7 1 × 7 1 1 = 2414 2^1 × 17^1 × 71^1 = 2414 2 1 × 1 7 1 × 7 1 1 = 2414 Through this we see that the LCM of 142 and 17 is 2414. How to Find the LCM of 142 and 17 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 142 and 17 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, 142 and 17: What are the Multiples of 142? What are the Multiples of 17? Let’s take a look at the first 10 multiples for each of these numbers, 142 and 17: First 10 Multiples of 142: 142, 284, 426, 568, 710, 852, 994, 1136, 1278, 1420 First 10 Multiples of 17: 17, 34, 51, 68, 85, 102, 119, 136, 153, 170 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 142 and 17 are 2414, 4828, 7242. Because 2414 is the smallest, it is the least common multiple. The LCM of 142 and 17 is 2414. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 24 and 76? What is the LCM of 42 and 127? What is the LCM of 6 and 117? What is the LCM of 78 and 43? What is the LCM of 8 and 106?