Q:

What is the LCM of 34 and 13?

Accepted Solution

A:
Solution: The LCM of 34 and 13 is 442 Methods How to find the LCM of 34 and 13 using Prime Factorization One way to find the LCM of 34 and 13 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 13? Here is the prime factorization of 34: 2 1 Γ— 1 7 1 2^1 Γ— 17^1 2 1 Γ— 1 7 1 And this is the prime factorization of 13: 1 3 1 13^1 1 3 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, 13 2 1 Γ— 1 3 1 Γ— 1 7 1 = 442 2^1 Γ— 13^1 Γ— 17^1 = 442 2 1 Γ— 1 3 1 Γ— 1 7 1 = 442 Through this we see that the LCM of 34 and 13 is 442. How to Find the LCM of 34 and 13 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 34 and 13 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 13: What are the Multiples of 34? What are the Multiples of 13? Let’s take a look at the first 10 multiples for each of these numbers, 34 and 13: First 10 Multiples of 34: 34, 68, 102, 136, 170, 204, 238, 272, 306, 340 First 10 Multiples of 13: 13, 26, 39, 52, 65, 78, 91, 104, 117, 130 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 13 are 442, 884, 1326. Because 442 is the smallest, it is the least common multiple. The LCM of 34 and 13 is 442. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 83 and 21? What is the LCM of 57 and 140? What is the LCM of 90 and 125? What is the LCM of 148 and 99? What is the LCM of 112 and 37?