Q:

What is the LCM of 111 and 67?

Accepted Solution

A:
Solution: The LCM of 111 and 67 is 7437 Methods How to find the LCM of 111 and 67 using Prime Factorization One way to find the LCM of 111 and 67 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 67? 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 67: 6 7 1 67^1 6 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: 3, 37, 67 3 1 × 3 7 1 × 6 7 1 = 7437 3^1 × 37^1 × 67^1 = 7437 3 1 × 3 7 1 × 6 7 1 = 7437 Through this we see that the LCM of 111 and 67 is 7437. How to Find the LCM of 111 and 67 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 111 and 67 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 67: What are the Multiples of 111? What are the Multiples of 67? Let’s take a look at the first 10 multiples for each of these numbers, 111 and 67: First 10 Multiples of 111: 111, 222, 333, 444, 555, 666, 777, 888, 999, 1110 First 10 Multiples of 67: 67, 134, 201, 268, 335, 402, 469, 536, 603, 670 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 67 are 7437, 14874, 22311. Because 7437 is the smallest, it is the least common multiple. The LCM of 111 and 67 is 7437. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 108 and 65? What is the LCM of 119 and 137? What is the LCM of 11 and 129? What is the LCM of 51 and 145? What is the LCM of 139 and 67?