Q:

What is the LCM of 38 and 76?

Accepted Solution

A:
Solution: The LCM of 38 and 76 is 76 Methods How to find the LCM of 38 and 76 using Prime Factorization One way to find the LCM of 38 and 76 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 76? 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 76: 2 2 × 1 9 1 2^2 × 19^1 2 2 × 1 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, 19 2 2 × 1 9 1 = 76 2^2 × 19^1 = 76 2 2 × 1 9 1 = 76 Through this we see that the LCM of 38 and 76 is 76. How to Find the LCM of 38 and 76 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 38 and 76 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 76: What are the Multiples of 38? What are the Multiples of 76? Let’s take a look at the first 10 multiples for each of these numbers, 38 and 76: First 10 Multiples of 38: 38, 76, 114, 152, 190, 228, 266, 304, 342, 380 First 10 Multiples of 76: 76, 152, 228, 304, 380, 456, 532, 608, 684, 760 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 76 are 76, 152, 228. Because 76 is the smallest, it is the least common multiple. The LCM of 38 and 76 is 76. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 133 and 117? What is the LCM of 72 and 140? What is the LCM of 59 and 50? What is the LCM of 12 and 110? What is the LCM of 113 and 13?