Q:

What is the LCM of 100 and 148?

Accepted Solution

A:
Solution: The LCM of 100 and 148 is 3700 Methods How to find the LCM of 100 and 148 using Prime Factorization One way to find the LCM of 100 and 148 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 100? What are the Factors of 148? Here is the prime factorization of 100: 2 2 × 5 2 2^2 × 5^2 2 2 × 5 2 And this is the prime factorization of 148: 2 2 × 3 7 1 2^2 × 37^1 2 2 × 3 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: 2, 5, 37 2 2 × 5 2 × 3 7 1 = 3700 2^2 × 5^2 × 37^1 = 3700 2 2 × 5 2 × 3 7 1 = 3700 Through this we see that the LCM of 100 and 148 is 3700. How to Find the LCM of 100 and 148 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 100 and 148 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, 100 and 148: What are the Multiples of 100? What are the Multiples of 148? Let’s take a look at the first 10 multiples for each of these numbers, 100 and 148: First 10 Multiples of 100: 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000 First 10 Multiples of 148: 148, 296, 444, 592, 740, 888, 1036, 1184, 1332, 1480 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 100 and 148 are 3700, 7400, 11100. Because 3700 is the smallest, it is the least common multiple. The LCM of 100 and 148 is 3700. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 26 and 103? What is the LCM of 141 and 57? What is the LCM of 20 and 22? What is the LCM of 143 and 1? What is the LCM of 16 and 12?