Q:

What is the LCM of 35 and 6?

Accepted Solution

A:
Solution: The LCM of 35 and 6 is 210 Methods How to find the LCM of 35 and 6 using Prime Factorization One way to find the LCM of 35 and 6 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 35? What are the Factors of 6? Here is the prime factorization of 35: 5 1 × 7 1 5^1 × 7^1 5 1 × 7 1 And this is the prime factorization of 6: 2 1 × 3 1 2^1 × 3^1 2 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: 5, 7, 2, 3 2 1 × 3 1 × 5 1 × 7 1 = 210 2^1 × 3^1 × 5^1 × 7^1 = 210 2 1 × 3 1 × 5 1 × 7 1 = 210 Through this we see that the LCM of 35 and 6 is 210. How to Find the LCM of 35 and 6 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 35 and 6 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, 35 and 6: What are the Multiples of 35? What are the Multiples of 6? Let’s take a look at the first 10 multiples for each of these numbers, 35 and 6: First 10 Multiples of 35: 35, 70, 105, 140, 175, 210, 245, 280, 315, 350 First 10 Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60 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 35 and 6 are 210, 420, 630. Because 210 is the smallest, it is the least common multiple. The LCM of 35 and 6 is 210. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 122 and 42? What is the LCM of 86 and 18? What is the LCM of 72 and 48? What is the LCM of 3 and 67? What is the LCM of 28 and 117?