Q:

What is the LCM of 119 and 27?

Accepted Solution

A:
Solution: The LCM of 119 and 27 is 3213 Methods How to find the LCM of 119 and 27 using Prime Factorization One way to find the LCM of 119 and 27 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 119? What are the Factors of 27? Here is the prime factorization of 119: 7 1 × 1 7 1 7^1 × 17^1 7 1 × 1 7 1 And this is the prime factorization of 27: 3 3 3^3 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: 7, 17, 3 3 3 × 7 1 × 1 7 1 = 3213 3^3 × 7^1 × 17^1 = 3213 3 3 × 7 1 × 1 7 1 = 3213 Through this we see that the LCM of 119 and 27 is 3213. How to Find the LCM of 119 and 27 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 119 and 27 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, 119 and 27: What are the Multiples of 119? What are the Multiples of 27? Let’s take a look at the first 10 multiples for each of these numbers, 119 and 27: First 10 Multiples of 119: 119, 238, 357, 476, 595, 714, 833, 952, 1071, 1190 First 10 Multiples of 27: 27, 54, 81, 108, 135, 162, 189, 216, 243, 270 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 119 and 27 are 3213, 6426, 9639. Because 3213 is the smallest, it is the least common multiple. The LCM of 119 and 27 is 3213. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 81 and 43? What is the LCM of 10 and 33? What is the LCM of 55 and 109? What is the LCM of 29 and 87? What is the LCM of 8 and 61?