Q:

What is the LCM of 147 and 16?

Accepted Solution

A:
Solution: The LCM of 147 and 16 is 2352 Methods How to find the LCM of 147 and 16 using Prime Factorization One way to find the LCM of 147 and 16 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 147? What are the Factors of 16? Here is the prime factorization of 147: 3 1 × 7 2 3^1 × 7^2 3 1 × 7 2 And this is the prime factorization of 16: 2 4 2^4 2 4 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, 7, 2 2 4 × 3 1 × 7 2 = 2352 2^4 × 3^1 × 7^2 = 2352 2 4 × 3 1 × 7 2 = 2352 Through this we see that the LCM of 147 and 16 is 2352. How to Find the LCM of 147 and 16 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 147 and 16 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, 147 and 16: What are the Multiples of 147? What are the Multiples of 16? Let’s take a look at the first 10 multiples for each of these numbers, 147 and 16: First 10 Multiples of 147: 147, 294, 441, 588, 735, 882, 1029, 1176, 1323, 1470 First 10 Multiples of 16: 16, 32, 48, 64, 80, 96, 112, 128, 144, 160 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 147 and 16 are 2352, 4704, 7056. Because 2352 is the smallest, it is the least common multiple. The LCM of 147 and 16 is 2352. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 5 and 98? What is the LCM of 13 and 150? What is the LCM of 80 and 127? What is the LCM of 92 and 81? What is the LCM of 21 and 88?