Q:

What is the LCM of 111 and 130?

Accepted Solution

A:
Solution: The LCM of 111 and 130 is 14430 Methods How to find the LCM of 111 and 130 using Prime Factorization One way to find the LCM of 111 and 130 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 111? What are the Factors of 130? Here is the prime factorization of 111: 3 1 × 3 7 1 3^1 × 37^1 3 1 × 3 7 1 And this is the prime factorization of 130: 2 1 × 5 1 × 1 3 1 2^1 × 5^1 × 13^1 2 1 × 5 1 × 1 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: 3, 37, 2, 5, 13 2 1 × 3 1 × 5 1 × 1 3 1 × 3 7 1 = 14430 2^1 × 3^1 × 5^1 × 13^1 × 37^1 = 14430 2 1 × 3 1 × 5 1 × 1 3 1 × 3 7 1 = 14430 Through this we see that the LCM of 111 and 130 is 14430. How to Find the LCM of 111 and 130 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 111 and 130 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, 111 and 130: What are the Multiples of 111? What are the Multiples of 130? Let’s take a look at the first 10 multiples for each of these numbers, 111 and 130: First 10 Multiples of 111: 111, 222, 333, 444, 555, 666, 777, 888, 999, 1110 First 10 Multiples of 130: 130, 260, 390, 520, 650, 780, 910, 1040, 1170, 1300 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 111 and 130 are 14430, 28860, 43290. Because 14430 is the smallest, it is the least common multiple. The LCM of 111 and 130 is 14430. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 147 and 132? What is the LCM of 27 and 44? What is the LCM of 53 and 47? What is the LCM of 72 and 29? What is the LCM of 14 and 66?