Q:

What is the LCM of 34 and 118?

Accepted Solution

A:
Solution: The LCM of 34 and 118 is 2006 Methods How to find the LCM of 34 and 118 using Prime Factorization One way to find the LCM of 34 and 118 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 34? What are the Factors of 118? Here is the prime factorization of 34: 2 1 × 1 7 1 2^1 × 17^1 2 1 × 1 7 1 And this is the prime factorization of 118: 2 1 × 5 9 1 2^1 × 59^1 2 1 × 5 9 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, 17, 59 2 1 × 1 7 1 × 5 9 1 = 2006 2^1 × 17^1 × 59^1 = 2006 2 1 × 1 7 1 × 5 9 1 = 2006 Through this we see that the LCM of 34 and 118 is 2006. How to Find the LCM of 34 and 118 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 34 and 118 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, 34 and 118: What are the Multiples of 34? What are the Multiples of 118? Let’s take a look at the first 10 multiples for each of these numbers, 34 and 118: First 10 Multiples of 34: 34, 68, 102, 136, 170, 204, 238, 272, 306, 340 First 10 Multiples of 118: 118, 236, 354, 472, 590, 708, 826, 944, 1062, 1180 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 34 and 118 are 2006, 4012, 6018. Because 2006 is the smallest, it is the least common multiple. The LCM of 34 and 118 is 2006. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 64 and 25? What is the LCM of 105 and 94? What is the LCM of 102 and 130? What is the LCM of 24 and 31? What is the LCM of 143 and 68?