Q:

What is the LCM of 118 and 12?

Accepted Solution

A:
Solution: The LCM of 118 and 12 is 708 Methods How to find the LCM of 118 and 12 using Prime Factorization One way to find the LCM of 118 and 12 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 118? What are the Factors of 12? Here is the prime factorization of 118: 2 1 × 5 9 1 2^1 × 59^1 2 1 × 5 9 1 And this is the prime factorization of 12: 2 2 × 3 1 2^2 × 3^1 2 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, 59, 3 2 2 × 3 1 × 5 9 1 = 708 2^2 × 3^1 × 59^1 = 708 2 2 × 3 1 × 5 9 1 = 708 Through this we see that the LCM of 118 and 12 is 708. How to Find the LCM of 118 and 12 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 118 and 12 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, 118 and 12: What are the Multiples of 118? What are the Multiples of 12? Let’s take a look at the first 10 multiples for each of these numbers, 118 and 12: First 10 Multiples of 118: 118, 236, 354, 472, 590, 708, 826, 944, 1062, 1180 First 10 Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120 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 118 and 12 are 708, 1416, 2124. Because 708 is the smallest, it is the least common multiple. The LCM of 118 and 12 is 708. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 142 and 33? What is the LCM of 56 and 57? What is the LCM of 98 and 20? What is the LCM of 103 and 29? What is the LCM of 42 and 127?