Q:

What is the LCM of 21 and 70?

Accepted Solution

A:
Solution: The LCM of 21 and 70 is 210 Methods How to find the LCM of 21 and 70 using Prime Factorization One way to find the LCM of 21 and 70 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 21? What are the Factors of 70? Here is the prime factorization of 21: 3 1 Γ— 7 1 3^1 Γ— 7^1 3 1 Γ— 7 1 And this is the prime factorization of 70: 2 1 Γ— 5 1 Γ— 7 1 2^1 Γ— 5^1 Γ— 7^1 2 1 Γ— 5 1 Γ— 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: 3, 7, 2, 5 2 1 Γ— 3 1 Γ— 5 1 Γ— 7 1 = 210 2^1 Γ— 3^1 Γ— 5^1 Γ— 7^1 = 210 2 1 Γ— 3 1 Γ— 5 1 Γ— 7 1 = 210 Through this we see that the LCM of 21 and 70 is 210. How to Find the LCM of 21 and 70 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 21 and 70 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, 21 and 70: What are the Multiples of 21? What are the Multiples of 70? Let’s take a look at the first 10 multiples for each of these numbers, 21 and 70: First 10 Multiples of 21: 21, 42, 63, 84, 105, 126, 147, 168, 189, 210 First 10 Multiples of 70: 70, 140, 210, 280, 350, 420, 490, 560, 630, 700 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 21 and 70 are 210, 420, 630. Because 210 is the smallest, it is the least common multiple. The LCM of 21 and 70 is 210. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 105 and 20? What is the LCM of 127 and 123? What is the LCM of 58 and 19? What is the LCM of 145 and 130? What is the LCM of 78 and 18?