Q:

What is the LCM of 67 and 20?

Accepted Solution

A:
Solution: The LCM of 67 and 20 is 1340 Methods How to find the LCM of 67 and 20 using Prime Factorization One way to find the LCM of 67 and 20 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 67? What are the Factors of 20? Here is the prime factorization of 67: 6 7 1 67^1 6 7 1 And this is the prime factorization of 20: 2 2 × 5 1 2^2 × 5^1 2 2 × 5 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: 67, 2, 5 2 2 × 5 1 × 6 7 1 = 1340 2^2 × 5^1 × 67^1 = 1340 2 2 × 5 1 × 6 7 1 = 1340 Through this we see that the LCM of 67 and 20 is 1340. How to Find the LCM of 67 and 20 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 67 and 20 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, 67 and 20: What are the Multiples of 67? What are the Multiples of 20? Let’s take a look at the first 10 multiples for each of these numbers, 67 and 20: First 10 Multiples of 67: 67, 134, 201, 268, 335, 402, 469, 536, 603, 670 First 10 Multiples of 20: 20, 40, 60, 80, 100, 120, 140, 160, 180, 200 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 67 and 20 are 1340, 2680, 4020. Because 1340 is the smallest, it is the least common multiple. The LCM of 67 and 20 is 1340. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 82 and 71? What is the LCM of 105 and 122? What is the LCM of 129 and 89? What is the LCM of 34 and 111? What is the LCM of 110 and 60?