Q:

What is the LCM of 104 and 38?

Accepted Solution

A:
Solution: The LCM of 104 and 38 is 1976 Methods How to find the LCM of 104 and 38 using Prime Factorization One way to find the LCM of 104 and 38 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 104? What are the Factors of 38? Here is the prime factorization of 104: 2 3 × 1 3 1 2^3 × 13^1 2 3 × 1 3 1 And this is the prime factorization of 38: 2 1 × 1 9 1 2^1 × 19^1 2 1 × 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, 13, 19 2 3 × 1 3 1 × 1 9 1 = 1976 2^3 × 13^1 × 19^1 = 1976 2 3 × 1 3 1 × 1 9 1 = 1976 Through this we see that the LCM of 104 and 38 is 1976. How to Find the LCM of 104 and 38 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 104 and 38 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, 104 and 38: What are the Multiples of 104? What are the Multiples of 38? Let’s take a look at the first 10 multiples for each of these numbers, 104 and 38: First 10 Multiples of 104: 104, 208, 312, 416, 520, 624, 728, 832, 936, 1040 First 10 Multiples of 38: 38, 76, 114, 152, 190, 228, 266, 304, 342, 380 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 104 and 38 are 1976, 3952, 5928. Because 1976 is the smallest, it is the least common multiple. The LCM of 104 and 38 is 1976. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 130 and 147? What is the LCM of 113 and 39? What is the LCM of 12 and 42? What is the LCM of 49 and 120? What is the LCM of 10 and 135?