Q:

What is the LCM of 123 and 147?

Accepted Solution

A:
Solution: The LCM of 123 and 147 is 6027 Methods How to find the LCM of 123 and 147 using Prime Factorization One way to find the LCM of 123 and 147 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 123? What are the Factors of 147? Here is the prime factorization of 123: 3 1 × 4 1 1 3^1 × 41^1 3 1 × 4 1 1 And this is the prime factorization of 147: 3 1 × 7 2 3^1 × 7^2 3 1 × 7 2 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: 3, 41, 7 3 1 × 7 2 × 4 1 1 = 6027 3^1 × 7^2 × 41^1 = 6027 3 1 × 7 2 × 4 1 1 = 6027 Through this we see that the LCM of 123 and 147 is 6027. How to Find the LCM of 123 and 147 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 123 and 147 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, 123 and 147: What are the Multiples of 123? What are the Multiples of 147? Let’s take a look at the first 10 multiples for each of these numbers, 123 and 147: First 10 Multiples of 123: 123, 246, 369, 492, 615, 738, 861, 984, 1107, 1230 First 10 Multiples of 147: 147, 294, 441, 588, 735, 882, 1029, 1176, 1323, 1470 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 123 and 147 are 6027, 12054, 18081. Because 6027 is the smallest, it is the least common multiple. The LCM of 123 and 147 is 6027. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 71 and 65? What is the LCM of 115 and 144? What is the LCM of 117 and 136? What is the LCM of 31 and 62? What is the LCM of 150 and 138?