Q:

What is the LCM of 19 and 148?

Accepted Solution

A:
Solution: The LCM of 19 and 148 is 2812 Methods How to find the LCM of 19 and 148 using Prime Factorization One way to find the LCM of 19 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 19? What are the Factors of 148? Here is the prime factorization of 19: 1 9 1 19^1 1 9 1 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: 19, 2, 37 2 2 × 1 9 1 × 3 7 1 = 2812 2^2 × 19^1 × 37^1 = 2812 2 2 × 1 9 1 × 3 7 1 = 2812 Through this we see that the LCM of 19 and 148 is 2812. How to Find the LCM of 19 and 148 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 19 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, 19 and 148: What are the Multiples of 19? What are the Multiples of 148? Let’s take a look at the first 10 multiples for each of these numbers, 19 and 148: First 10 Multiples of 19: 19, 38, 57, 76, 95, 114, 133, 152, 171, 190 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 19 and 148 are 2812, 5624, 8436. Because 2812 is the smallest, it is the least common multiple. The LCM of 19 and 148 is 2812. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 116 and 132? What is the LCM of 78 and 61? What is the LCM of 76 and 150? What is the LCM of 111 and 55? What is the LCM of 26 and 60?