Q:

What is the LCM of 115 and 54?

Accepted Solution

A:
Solution: The LCM of 115 and 54 is 6210 Methods How to find the LCM of 115 and 54 using Prime Factorization One way to find the LCM of 115 and 54 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 115? What are the Factors of 54? Here is the prime factorization of 115: 5 1 × 2 3 1 5^1 × 23^1 5 1 × 2 3 1 And this is the prime factorization of 54: 2 1 × 3 3 2^1 × 3^3 2 1 × 3 3 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: 5, 23, 2, 3 2 1 × 3 3 × 5 1 × 2 3 1 = 6210 2^1 × 3^3 × 5^1 × 23^1 = 6210 2 1 × 3 3 × 5 1 × 2 3 1 = 6210 Through this we see that the LCM of 115 and 54 is 6210. How to Find the LCM of 115 and 54 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 115 and 54 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, 115 and 54: What are the Multiples of 115? What are the Multiples of 54? Let’s take a look at the first 10 multiples for each of these numbers, 115 and 54: First 10 Multiples of 115: 115, 230, 345, 460, 575, 690, 805, 920, 1035, 1150 First 10 Multiples of 54: 54, 108, 162, 216, 270, 324, 378, 432, 486, 540 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 115 and 54 are 6210, 12420, 18630. Because 6210 is the smallest, it is the least common multiple. The LCM of 115 and 54 is 6210. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 11 and 44? What is the LCM of 28 and 74? What is the LCM of 63 and 114? What is the LCM of 67 and 29? What is the LCM of 99 and 143?