Q:

What is the LCM of 49 and 104?

Accepted Solution

A:
Solution: The LCM of 49 and 104 is 5096 Methods How to find the LCM of 49 and 104 using Prime Factorization One way to find the LCM of 49 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 49? What are the Factors of 104? Here is the prime factorization of 49: 7 2 7^2 7 2 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: 7, 2, 13 2 3 × 7 2 × 1 3 1 = 5096 2^3 × 7^2 × 13^1 = 5096 2 3 × 7 2 × 1 3 1 = 5096 Through this we see that the LCM of 49 and 104 is 5096. How to Find the LCM of 49 and 104 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 49 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, 49 and 104: What are the Multiples of 49? What are the Multiples of 104? Let’s take a look at the first 10 multiples for each of these numbers, 49 and 104: First 10 Multiples of 49: 49, 98, 147, 196, 245, 294, 343, 392, 441, 490 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 49 and 104 are 5096, 10192, 15288. Because 5096 is the smallest, it is the least common multiple. The LCM of 49 and 104 is 5096. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 23 and 135? What is the LCM of 86 and 33? What is the LCM of 20 and 29? What is the LCM of 41 and 59? What is the LCM of 105 and 32?