Q:

What is the LCM of 148 and 78?

Accepted Solution

A:
Solution: The LCM of 148 and 78 is 5772 Methods How to find the LCM of 148 and 78 using Prime Factorization One way to find the LCM of 148 and 78 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 78? 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 78: 2 1 × 3 1 × 1 3 1 2^1 × 3^1 × 13^1 2 1 × 3 1 × 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: 2, 37, 3, 13 2 2 × 3 1 × 1 3 1 × 3 7 1 = 5772 2^2 × 3^1 × 13^1 × 37^1 = 5772 2 2 × 3 1 × 1 3 1 × 3 7 1 = 5772 Through this we see that the LCM of 148 and 78 is 5772. How to Find the LCM of 148 and 78 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 148 and 78 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 78: What are the Multiples of 148? What are the Multiples of 78? Let’s take a look at the first 10 multiples for each of these numbers, 148 and 78: First 10 Multiples of 148: 148, 296, 444, 592, 740, 888, 1036, 1184, 1332, 1480 First 10 Multiples of 78: 78, 156, 234, 312, 390, 468, 546, 624, 702, 780 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 78 are 5772, 11544, 17316. Because 5772 is the smallest, it is the least common multiple. The LCM of 148 and 78 is 5772. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 114 and 34? What is the LCM of 15 and 22? What is the LCM of 124 and 139? What is the LCM of 115 and 144? What is the LCM of 109 and 35?