Q:

What is the LCM of 38 and 10?

Accepted Solution

A:
Solution: The LCM of 38 and 10 is 190 Methods How to find the LCM of 38 and 10 using Prime Factorization One way to find the LCM of 38 and 10 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 10? 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 10: 2 1 × 5 1 2^1 × 5^1 2 1 × 5 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 2 1 × 5 1 × 1 9 1 = 190 2^1 × 5^1 × 19^1 = 190 2 1 × 5 1 × 1 9 1 = 190 Through this we see that the LCM of 38 and 10 is 190. How to Find the LCM of 38 and 10 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 38 and 10 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 10: What are the Multiples of 38? What are the Multiples of 10? Let’s take a look at the first 10 multiples for each of these numbers, 38 and 10: First 10 Multiples of 38: 38, 76, 114, 152, 190, 228, 266, 304, 342, 380 First 10 Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 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 10 are 190, 380, 570. Because 190 is the smallest, it is the least common multiple. The LCM of 38 and 10 is 190. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 6 and 61? What is the LCM of 26 and 140? What is the LCM of 44 and 1? What is the LCM of 48 and 43? What is the LCM of 150 and 71?