Q:

What is the LCM of 68 and 105?

Accepted Solution

A:
Solution: The LCM of 68 and 105 is 7140 Methods How to find the LCM of 68 and 105 using Prime Factorization One way to find the LCM of 68 and 105 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 68? What are the Factors of 105? Here is the prime factorization of 68: 2 2 × 1 7 1 2^2 × 17^1 2 2 × 1 7 1 And this is the prime factorization of 105: 3 1 × 5 1 × 7 1 3^1 × 5^1 × 7^1 3 1 × 5 1 × 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, 17, 3, 5, 7 2 2 × 3 1 × 5 1 × 7 1 × 1 7 1 = 7140 2^2 × 3^1 × 5^1 × 7^1 × 17^1 = 7140 2 2 × 3 1 × 5 1 × 7 1 × 1 7 1 = 7140 Through this we see that the LCM of 68 and 105 is 7140. How to Find the LCM of 68 and 105 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 68 and 105 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, 68 and 105: What are the Multiples of 68? What are the Multiples of 105? Let’s take a look at the first 10 multiples for each of these numbers, 68 and 105: First 10 Multiples of 68: 68, 136, 204, 272, 340, 408, 476, 544, 612, 680 First 10 Multiples of 105: 105, 210, 315, 420, 525, 630, 735, 840, 945, 1050 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 68 and 105 are 7140, 14280, 21420. Because 7140 is the smallest, it is the least common multiple. The LCM of 68 and 105 is 7140. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 15 and 66? What is the LCM of 43 and 110? What is the LCM of 94 and 11? What is the LCM of 131 and 65? What is the LCM of 18 and 83?