Q:

What is the LCM of 26 and 30?

Accepted Solution

A:
Solution: The LCM of 26 and 30 is 390 Methods How to find the LCM of 26 and 30 using Prime Factorization One way to find the LCM of 26 and 30 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 26? What are the Factors of 30? Here is the prime factorization of 26: 2 1 × 1 3 1 2^1 × 13^1 2 1 × 1 3 1 And this is the prime factorization of 30: 2 1 × 3 1 × 5 1 2^1 × 3^1 × 5^1 2 1 × 3 1 × 5 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, 13, 3, 5 2 1 × 3 1 × 5 1 × 1 3 1 = 390 2^1 × 3^1 × 5^1 × 13^1 = 390 2 1 × 3 1 × 5 1 × 1 3 1 = 390 Through this we see that the LCM of 26 and 30 is 390. How to Find the LCM of 26 and 30 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 26 and 30 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, 26 and 30: What are the Multiples of 26? What are the Multiples of 30? Let’s take a look at the first 10 multiples for each of these numbers, 26 and 30: First 10 Multiples of 26: 26, 52, 78, 104, 130, 156, 182, 208, 234, 260 First 10 Multiples of 30: 30, 60, 90, 120, 150, 180, 210, 240, 270, 300 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 26 and 30 are 390, 780, 1170. Because 390 is the smallest, it is the least common multiple. The LCM of 26 and 30 is 390. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 93 and 16? What is the LCM of 124 and 46? What is the LCM of 83 and 55? What is the LCM of 78 and 12? What is the LCM of 5 and 140?