Q:

What is the LCM of 65 and 55?

Accepted Solution

A:
Solution: The LCM of 65 and 55 is 715 Methods How to find the LCM of 65 and 55 using Prime Factorization One way to find the LCM of 65 and 55 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 65? What are the Factors of 55? Here is the prime factorization of 65: 5 1 × 1 3 1 5^1 × 13^1 5 1 × 1 3 1 And this is the prime factorization of 55: 5 1 × 1 1 1 5^1 × 11^1 5 1 × 1 1 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: 5, 13, 11 5 1 × 1 1 1 × 1 3 1 = 715 5^1 × 11^1 × 13^1 = 715 5 1 × 1 1 1 × 1 3 1 = 715 Through this we see that the LCM of 65 and 55 is 715. How to Find the LCM of 65 and 55 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 65 and 55 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, 65 and 55: What are the Multiples of 65? What are the Multiples of 55? Let’s take a look at the first 10 multiples for each of these numbers, 65 and 55: First 10 Multiples of 65: 65, 130, 195, 260, 325, 390, 455, 520, 585, 650 First 10 Multiples of 55: 55, 110, 165, 220, 275, 330, 385, 440, 495, 550 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 65 and 55 are 715, 1430, 2145. Because 715 is the smallest, it is the least common multiple. The LCM of 65 and 55 is 715. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 135 and 69? What is the LCM of 137 and 19? What is the LCM of 63 and 96? What is the LCM of 26 and 147? What is the LCM of 73 and 3?