Q:

What is the LCM of 114 and 65?

Accepted Solution

A:
Solution: The LCM of 114 and 65 is 7410 Methods How to find the LCM of 114 and 65 using Prime Factorization One way to find the LCM of 114 and 65 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 114? What are the Factors of 65? Here is the prime factorization of 114: 2 1 × 3 1 × 1 9 1 2^1 × 3^1 × 19^1 2 1 × 3 1 × 1 9 1 And this is the prime factorization of 65: 5 1 × 1 3 1 5^1 × 13^1 5 1 × 1 3 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, 3, 19, 5, 13 2 1 × 3 1 × 5 1 × 1 3 1 × 1 9 1 = 7410 2^1 × 3^1 × 5^1 × 13^1 × 19^1 = 7410 2 1 × 3 1 × 5 1 × 1 3 1 × 1 9 1 = 7410 Through this we see that the LCM of 114 and 65 is 7410. How to Find the LCM of 114 and 65 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 114 and 65 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, 114 and 65: What are the Multiples of 114? What are the Multiples of 65? Let’s take a look at the first 10 multiples for each of these numbers, 114 and 65: First 10 Multiples of 114: 114, 228, 342, 456, 570, 684, 798, 912, 1026, 1140 First 10 Multiples of 65: 65, 130, 195, 260, 325, 390, 455, 520, 585, 650 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 114 and 65 are 7410, 14820, 22230. Because 7410 is the smallest, it is the least common multiple. The LCM of 114 and 65 is 7410. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 76 and 17? What is the LCM of 81 and 145? What is the LCM of 117 and 139? What is the LCM of 84 and 90? What is the LCM of 91 and 70?