Q:

What is the LCM of 70 and 130?

Accepted Solution

A:
Solution: The LCM of 70 and 130 is 910 Methods How to find the LCM of 70 and 130 using Prime Factorization One way to find the LCM of 70 and 130 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 70? What are the Factors of 130? Here is the prime factorization of 70: 2 1 × 5 1 × 7 1 2^1 × 5^1 × 7^1 2 1 × 5 1 × 7 1 And this is the prime factorization of 130: 2 1 × 5 1 × 1 3 1 2^1 × 5^1 × 13^1 2 1 × 5 1 × 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: 2, 5, 7, 13 2 1 × 5 1 × 7 1 × 1 3 1 = 910 2^1 × 5^1 × 7^1 × 13^1 = 910 2 1 × 5 1 × 7 1 × 1 3 1 = 910 Through this we see that the LCM of 70 and 130 is 910. How to Find the LCM of 70 and 130 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 70 and 130 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, 70 and 130: What are the Multiples of 70? What are the Multiples of 130? Let’s take a look at the first 10 multiples for each of these numbers, 70 and 130: First 10 Multiples of 70: 70, 140, 210, 280, 350, 420, 490, 560, 630, 700 First 10 Multiples of 130: 130, 260, 390, 520, 650, 780, 910, 1040, 1170, 1300 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 70 and 130 are 910, 1820, 2730. Because 910 is the smallest, it is the least common multiple. The LCM of 70 and 130 is 910. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 41 and 107? What is the LCM of 83 and 122? What is the LCM of 6 and 60? What is the LCM of 103 and 12? What is the LCM of 149 and 42?