Q:

What is the LCM of 101 and 40?

Accepted Solution

A:
Solution: The LCM of 101 and 40 is 4040 Methods How to find the LCM of 101 and 40 using Prime Factorization One way to find the LCM of 101 and 40 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 101? What are the Factors of 40? Here is the prime factorization of 101: 10 1 1 101^1 10 1 1 And this is the prime factorization of 40: 2 3 × 5 1 2^3 × 5^1 2 3 × 5 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: 101, 2, 5 2 3 × 5 1 × 10 1 1 = 4040 2^3 × 5^1 × 101^1 = 4040 2 3 × 5 1 × 10 1 1 = 4040 Through this we see that the LCM of 101 and 40 is 4040. How to Find the LCM of 101 and 40 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 101 and 40 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, 101 and 40: What are the Multiples of 101? What are the Multiples of 40? Let’s take a look at the first 10 multiples for each of these numbers, 101 and 40: First 10 Multiples of 101: 101, 202, 303, 404, 505, 606, 707, 808, 909, 1010 First 10 Multiples of 40: 40, 80, 120, 160, 200, 240, 280, 320, 360, 400 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 101 and 40 are 4040, 8080, 12120. Because 4040 is the smallest, it is the least common multiple. The LCM of 101 and 40 is 4040. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 28 and 78? What is the LCM of 18 and 140? What is the LCM of 31 and 129? What is the LCM of 19 and 13? What is the LCM of 108 and 120?