Q:

What is the LCM of 25 and 137?

Accepted Solution

A:
Solution: The LCM of 25 and 137 is 3425 Methods How to find the LCM of 25 and 137 using Prime Factorization One way to find the LCM of 25 and 137 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 25? What are the Factors of 137? Here is the prime factorization of 25: 5 2 5^2 5 2 And this is the prime factorization of 137: 13 7 1 137^1 13 7 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: 5, 137 5 2 × 13 7 1 = 3425 5^2 × 137^1 = 3425 5 2 × 13 7 1 = 3425 Through this we see that the LCM of 25 and 137 is 3425. How to Find the LCM of 25 and 137 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 25 and 137 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, 25 and 137: What are the Multiples of 25? What are the Multiples of 137? Let’s take a look at the first 10 multiples for each of these numbers, 25 and 137: First 10 Multiples of 25: 25, 50, 75, 100, 125, 150, 175, 200, 225, 250 First 10 Multiples of 137: 137, 274, 411, 548, 685, 822, 959, 1096, 1233, 1370 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 25 and 137 are 3425, 6850, 10275. Because 3425 is the smallest, it is the least common multiple. The LCM of 25 and 137 is 3425. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 71 and 37? What is the LCM of 2 and 77? What is the LCM of 8 and 35? What is the LCM of 144 and 74? What is the LCM of 111 and 136?