Q:

What is the LCM of 56 and 104?

Accepted Solution

A:
Solution: The LCM of 56 and 104 is 728 Methods How to find the LCM of 56 and 104 using Prime Factorization One way to find the LCM of 56 and 104 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 56? What are the Factors of 104? Here is the prime factorization of 56: 2 3 × 7 1 2^3 × 7^1 2 3 × 7 1 And this is the prime factorization of 104: 2 3 × 1 3 1 2^3 × 13^1 2 3 × 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, 7, 13 2 3 × 7 1 × 1 3 1 = 728 2^3 × 7^1 × 13^1 = 728 2 3 × 7 1 × 1 3 1 = 728 Through this we see that the LCM of 56 and 104 is 728. How to Find the LCM of 56 and 104 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 56 and 104 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, 56 and 104: What are the Multiples of 56? What are the Multiples of 104? Let’s take a look at the first 10 multiples for each of these numbers, 56 and 104: First 10 Multiples of 56: 56, 112, 168, 224, 280, 336, 392, 448, 504, 560 First 10 Multiples of 104: 104, 208, 312, 416, 520, 624, 728, 832, 936, 1040 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 56 and 104 are 728, 1456, 2184. Because 728 is the smallest, it is the least common multiple. The LCM of 56 and 104 is 728. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 32 and 79? What is the LCM of 119 and 55? What is the LCM of 122 and 14? What is the LCM of 141 and 88? What is the LCM of 110 and 126?