Q:

What is the LCM of 132 and 47?

Accepted Solution

A:
Solution: The LCM of 132 and 47 is 6204 Methods How to find the LCM of 132 and 47 using Prime Factorization One way to find the LCM of 132 and 47 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 132? What are the Factors of 47? Here is the prime factorization of 132: 2 2 × 3 1 × 1 1 1 2^2 × 3^1 × 11^1 2 2 × 3 1 × 1 1 1 And this is the prime factorization of 47: 4 7 1 47^1 4 7 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, 3, 11, 47 2 2 × 3 1 × 1 1 1 × 4 7 1 = 6204 2^2 × 3^1 × 11^1 × 47^1 = 6204 2 2 × 3 1 × 1 1 1 × 4 7 1 = 6204 Through this we see that the LCM of 132 and 47 is 6204. How to Find the LCM of 132 and 47 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 132 and 47 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, 132 and 47: What are the Multiples of 132? What are the Multiples of 47? Let’s take a look at the first 10 multiples for each of these numbers, 132 and 47: First 10 Multiples of 132: 132, 264, 396, 528, 660, 792, 924, 1056, 1188, 1320 First 10 Multiples of 47: 47, 94, 141, 188, 235, 282, 329, 376, 423, 470 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 132 and 47 are 6204, 12408, 18612. Because 6204 is the smallest, it is the least common multiple. The LCM of 132 and 47 is 6204. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 112 and 90? What is the LCM of 74 and 138? What is the LCM of 84 and 72? What is the LCM of 45 and 149? What is the LCM of 52 and 1?