Q:

What is the LCM of 16 and 35?

Accepted Solution

A:
Solution: The LCM of 16 and 35 is 560 Methods How to find the LCM of 16 and 35 using Prime Factorization One way to find the LCM of 16 and 35 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 16? What are the Factors of 35? Here is the prime factorization of 16: 2 4 2^4 2 4 And this is the prime factorization of 35: 5 1 × 7 1 5^1 × 7^1 5 1 × 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: 2, 5, 7 2 4 × 5 1 × 7 1 = 560 2^4 × 5^1 × 7^1 = 560 2 4 × 5 1 × 7 1 = 560 Through this we see that the LCM of 16 and 35 is 560. How to Find the LCM of 16 and 35 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 16 and 35 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, 16 and 35: What are the Multiples of 16? What are the Multiples of 35? Let’s take a look at the first 10 multiples for each of these numbers, 16 and 35: First 10 Multiples of 16: 16, 32, 48, 64, 80, 96, 112, 128, 144, 160 First 10 Multiples of 35: 35, 70, 105, 140, 175, 210, 245, 280, 315, 350 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 16 and 35 are 560, 1120, 1680. Because 560 is the smallest, it is the least common multiple. The LCM of 16 and 35 is 560. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 12 and 30? What is the LCM of 91 and 46? What is the LCM of 17 and 82? What is the LCM of 71 and 150? What is the LCM of 79 and 49?