Q:

What is the LCM of 19 and 67?

Accepted Solution

A:
Solution: The LCM of 19 and 67 is 1273 Methods How to find the LCM of 19 and 67 using Prime Factorization One way to find the LCM of 19 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 19? What are the Factors of 67? Here is the prime factorization of 19: 1 9 1 19^1 1 9 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: 19, 67 1 9 1 × 6 7 1 = 1273 19^1 × 67^1 = 1273 1 9 1 × 6 7 1 = 1273 Through this we see that the LCM of 19 and 67 is 1273. How to Find the LCM of 19 and 67 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 19 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, 19 and 67: What are the Multiples of 19? What are the Multiples of 67? Let’s take a look at the first 10 multiples for each of these numbers, 19 and 67: First 10 Multiples of 19: 19, 38, 57, 76, 95, 114, 133, 152, 171, 190 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 19 and 67 are 1273, 2546, 3819. Because 1273 is the smallest, it is the least common multiple. The LCM of 19 and 67 is 1273. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 114 and 60? What is the LCM of 39 and 149? What is the LCM of 82 and 85? What is the LCM of 135 and 129? What is the LCM of 131 and 143?