Q:

What is the LCM of 148 and 68?

Accepted Solution

A:
Solution: The LCM of 148 and 68 is 2516 Methods How to find the LCM of 148 and 68 using Prime Factorization One way to find the LCM of 148 and 68 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 148? What are the Factors of 68? Here is the prime factorization of 148: 2 2 × 3 7 1 2^2 × 37^1 2 2 × 3 7 1 And this is the prime factorization of 68: 2 2 × 1 7 1 2^2 × 17^1 2 2 × 1 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, 37, 17 2 2 × 1 7 1 × 3 7 1 = 2516 2^2 × 17^1 × 37^1 = 2516 2 2 × 1 7 1 × 3 7 1 = 2516 Through this we see that the LCM of 148 and 68 is 2516. How to Find the LCM of 148 and 68 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 148 and 68 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, 148 and 68: What are the Multiples of 148? What are the Multiples of 68? Let’s take a look at the first 10 multiples for each of these numbers, 148 and 68: First 10 Multiples of 148: 148, 296, 444, 592, 740, 888, 1036, 1184, 1332, 1480 First 10 Multiples of 68: 68, 136, 204, 272, 340, 408, 476, 544, 612, 680 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 148 and 68 are 2516, 5032, 7548. Because 2516 is the smallest, it is the least common multiple. The LCM of 148 and 68 is 2516. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 20 and 81? What is the LCM of 121 and 55? What is the LCM of 28 and 10? What is the LCM of 49 and 132? What is the LCM of 40 and 24?