Q:

What is the LCM of 10 and 49?

Accepted Solution

A:
Solution: The LCM of 10 and 49 is 490 Methods How to find the LCM of 10 and 49 using Prime Factorization One way to find the LCM of 10 and 49 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 10? What are the Factors of 49? Here is the prime factorization of 10: 2 1 × 5 1 2^1 × 5^1 2 1 × 5 1 And this is the prime factorization of 49: 7 2 7^2 7 2 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 1 × 5 1 × 7 2 = 490 2^1 × 5^1 × 7^2 = 490 2 1 × 5 1 × 7 2 = 490 Through this we see that the LCM of 10 and 49 is 490. How to Find the LCM of 10 and 49 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 10 and 49 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, 10 and 49: What are the Multiples of 10? What are the Multiples of 49? Let’s take a look at the first 10 multiples for each of these numbers, 10 and 49: First 10 Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 First 10 Multiples of 49: 49, 98, 147, 196, 245, 294, 343, 392, 441, 490 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 10 and 49 are 490, 980, 1470. Because 490 is the smallest, it is the least common multiple. The LCM of 10 and 49 is 490. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 42 and 29? What is the LCM of 30 and 56? What is the LCM of 142 and 108? What is the LCM of 67 and 82? What is the LCM of 33 and 109?