Q:

What is the LCM of 26 and 114?

Accepted Solution

A:
Solution: The LCM of 26 and 114 is 1482 Methods How to find the LCM of 26 and 114 using Prime Factorization One way to find the LCM of 26 and 114 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 114? 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 114: 2 1 × 3 1 × 1 9 1 2^1 × 3^1 × 19^1 2 1 × 3 1 × 1 9 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, 19 2 1 × 3 1 × 1 3 1 × 1 9 1 = 1482 2^1 × 3^1 × 13^1 × 19^1 = 1482 2 1 × 3 1 × 1 3 1 × 1 9 1 = 1482 Through this we see that the LCM of 26 and 114 is 1482. How to Find the LCM of 26 and 114 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 26 and 114 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 114: What are the Multiples of 26? What are the Multiples of 114? Let’s take a look at the first 10 multiples for each of these numbers, 26 and 114: First 10 Multiples of 26: 26, 52, 78, 104, 130, 156, 182, 208, 234, 260 First 10 Multiples of 114: 114, 228, 342, 456, 570, 684, 798, 912, 1026, 1140 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 114 are 1482, 2964, 4446. Because 1482 is the smallest, it is the least common multiple. The LCM of 26 and 114 is 1482. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 50 and 138? What is the LCM of 95 and 132? What is the LCM of 129 and 73? What is the LCM of 55 and 41? What is the LCM of 104 and 146?