Q:

What is the LCM of 60 and 46?

Accepted Solution

A:
Solution: The LCM of 60 and 46 is 1380 Methods How to find the LCM of 60 and 46 using Prime Factorization One way to find the LCM of 60 and 46 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 60? What are the Factors of 46? Here is the prime factorization of 60: 2 2 × 3 1 × 5 1 2^2 × 3^1 × 5^1 2 2 × 3 1 × 5 1 And this is the prime factorization of 46: 2 1 × 2 3 1 2^1 × 23^1 2 1 × 2 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, 3, 5, 23 2 2 × 3 1 × 5 1 × 2 3 1 = 1380 2^2 × 3^1 × 5^1 × 23^1 = 1380 2 2 × 3 1 × 5 1 × 2 3 1 = 1380 Through this we see that the LCM of 60 and 46 is 1380. How to Find the LCM of 60 and 46 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 60 and 46 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, 60 and 46: What are the Multiples of 60? What are the Multiples of 46? Let’s take a look at the first 10 multiples for each of these numbers, 60 and 46: First 10 Multiples of 60: 60, 120, 180, 240, 300, 360, 420, 480, 540, 600 First 10 Multiples of 46: 46, 92, 138, 184, 230, 276, 322, 368, 414, 460 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 60 and 46 are 1380, 2760, 4140. Because 1380 is the smallest, it is the least common multiple. The LCM of 60 and 46 is 1380. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 116 and 83? What is the LCM of 124 and 115? What is the LCM of 118 and 141? What is the LCM of 98 and 25? What is the LCM of 93 and 100?