Q:

What is the LCM of 127 and 12?

Accepted Solution

A:
Solution: The LCM of 127 and 12 is 1524 Methods How to find the LCM of 127 and 12 using Prime Factorization One way to find the LCM of 127 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 127? What are the Factors of 12? Here is the prime factorization of 127: 12 7 1 127^1 12 7 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: 127, 2, 3 2 2 × 3 1 × 12 7 1 = 1524 2^2 × 3^1 × 127^1 = 1524 2 2 × 3 1 × 12 7 1 = 1524 Through this we see that the LCM of 127 and 12 is 1524. How to Find the LCM of 127 and 12 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 127 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, 127 and 12: What are the Multiples of 127? What are the Multiples of 12? Let’s take a look at the first 10 multiples for each of these numbers, 127 and 12: First 10 Multiples of 127: 127, 254, 381, 508, 635, 762, 889, 1016, 1143, 1270 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 127 and 12 are 1524, 3048, 4572. Because 1524 is the smallest, it is the least common multiple. The LCM of 127 and 12 is 1524. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 53 and 77? What is the LCM of 114 and 56? What is the LCM of 70 and 37? What is the LCM of 59 and 33? What is the LCM of 10 and 131?