Q:

What is the LCM of 101 and 132?

Accepted Solution

A:
Solution: The LCM of 101 and 132 is 13332 Methods How to find the LCM of 101 and 132 using Prime Factorization One way to find the LCM of 101 and 132 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 101? What are the Factors of 132? Here is the prime factorization of 101: 10 1 1 101^1 10 1 1 And this 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 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: 101, 2, 3, 11 2 2 × 3 1 × 1 1 1 × 10 1 1 = 13332 2^2 × 3^1 × 11^1 × 101^1 = 13332 2 2 × 3 1 × 1 1 1 × 10 1 1 = 13332 Through this we see that the LCM of 101 and 132 is 13332. How to Find the LCM of 101 and 132 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 101 and 132 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, 101 and 132: What are the Multiples of 101? What are the Multiples of 132? Let’s take a look at the first 10 multiples for each of these numbers, 101 and 132: First 10 Multiples of 101: 101, 202, 303, 404, 505, 606, 707, 808, 909, 1010 First 10 Multiples of 132: 132, 264, 396, 528, 660, 792, 924, 1056, 1188, 1320 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 101 and 132 are 13332, 26664, 39996. Because 13332 is the smallest, it is the least common multiple. The LCM of 101 and 132 is 13332. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 5 and 106? What is the LCM of 11 and 26? What is the LCM of 18 and 82? What is the LCM of 74 and 25? What is the LCM of 124 and 132?