Q:

What is the LCM of 106 and 15?

Accepted Solution

A:
Solution: The LCM of 106 and 15 is 1590 Methods How to find the LCM of 106 and 15 using Prime Factorization One way to find the LCM of 106 and 15 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 106? What are the Factors of 15? Here is the prime factorization of 106: 2 1 × 5 3 1 2^1 × 53^1 2 1 × 5 3 1 And this is the prime factorization of 15: 3 1 × 5 1 3^1 × 5^1 3 1 × 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: 2, 53, 3, 5 2 1 × 3 1 × 5 1 × 5 3 1 = 1590 2^1 × 3^1 × 5^1 × 53^1 = 1590 2 1 × 3 1 × 5 1 × 5 3 1 = 1590 Through this we see that the LCM of 106 and 15 is 1590. How to Find the LCM of 106 and 15 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 106 and 15 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, 106 and 15: What are the Multiples of 106? What are the Multiples of 15? Let’s take a look at the first 10 multiples for each of these numbers, 106 and 15: First 10 Multiples of 106: 106, 212, 318, 424, 530, 636, 742, 848, 954, 1060 First 10 Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150 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 106 and 15 are 1590, 3180, 4770. Because 1590 is the smallest, it is the least common multiple. The LCM of 106 and 15 is 1590. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 61 and 137? What is the LCM of 84 and 103? What is the LCM of 101 and 5? What is the LCM of 8 and 17? What is the LCM of 78 and 34?