Q:

What is the LCM of 38 and 65?

Accepted Solution

A:
Solution: The LCM of 38 and 65 is 2470 Methods How to find the LCM of 38 and 65 using Prime Factorization One way to find the LCM of 38 and 65 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 38? What are the Factors of 65? Here is the prime factorization of 38: 2 1 × 1 9 1 2^1 × 19^1 2 1 × 1 9 1 And this is the prime factorization of 65: 5 1 × 1 3 1 5^1 × 13^1 5 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, 19, 5, 13 2 1 × 5 1 × 1 3 1 × 1 9 1 = 2470 2^1 × 5^1 × 13^1 × 19^1 = 2470 2 1 × 5 1 × 1 3 1 × 1 9 1 = 2470 Through this we see that the LCM of 38 and 65 is 2470. How to Find the LCM of 38 and 65 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 38 and 65 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, 38 and 65: What are the Multiples of 38? What are the Multiples of 65? Let’s take a look at the first 10 multiples for each of these numbers, 38 and 65: First 10 Multiples of 38: 38, 76, 114, 152, 190, 228, 266, 304, 342, 380 First 10 Multiples of 65: 65, 130, 195, 260, 325, 390, 455, 520, 585, 650 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 38 and 65 are 2470, 4940, 7410. Because 2470 is the smallest, it is the least common multiple. The LCM of 38 and 65 is 2470. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 99 and 109? What is the LCM of 128 and 117? What is the LCM of 150 and 148? What is the LCM of 98 and 106? What is the LCM of 84 and 78?