Q:

What is the LCM of 17 and 88?

Accepted Solution

A:
Solution: The LCM of 17 and 88 is 1496 Methods How to find the LCM of 17 and 88 using Prime Factorization One way to find the LCM of 17 and 88 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 17? What are the Factors of 88? Here is the prime factorization of 17: 1 7 1 17^1 1 7 1 And this is the prime factorization of 88: 2 3 × 1 1 1 2^3 × 11^1 2 3 × 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: 17, 2, 11 2 3 × 1 1 1 × 1 7 1 = 1496 2^3 × 11^1 × 17^1 = 1496 2 3 × 1 1 1 × 1 7 1 = 1496 Through this we see that the LCM of 17 and 88 is 1496. How to Find the LCM of 17 and 88 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 17 and 88 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, 17 and 88: What are the Multiples of 17? What are the Multiples of 88? Let’s take a look at the first 10 multiples for each of these numbers, 17 and 88: First 10 Multiples of 17: 17, 34, 51, 68, 85, 102, 119, 136, 153, 170 First 10 Multiples of 88: 88, 176, 264, 352, 440, 528, 616, 704, 792, 880 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 17 and 88 are 1496, 2992, 4488. Because 1496 is the smallest, it is the least common multiple. The LCM of 17 and 88 is 1496. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 29 and 3? What is the LCM of 18 and 126? What is the LCM of 143 and 77? What is the LCM of 49 and 78? What is the LCM of 24 and 12?