Q:

What is the LCM of 40 and 150?

Accepted Solution

A:
Solution: The LCM of 40 and 150 is 600 Methods How to find the LCM of 40 and 150 using Prime Factorization One way to find the LCM of 40 and 150 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 40? What are the Factors of 150? Here is the prime factorization of 40: 2 3 × 5 1 2^3 × 5^1 2 3 × 5 1 And this is the prime factorization of 150: 2 1 × 3 1 × 5 2 2^1 × 3^1 × 5^2 2 1 × 3 1 × 5 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, 3 2 3 × 3 1 × 5 2 = 600 2^3 × 3^1 × 5^2 = 600 2 3 × 3 1 × 5 2 = 600 Through this we see that the LCM of 40 and 150 is 600. How to Find the LCM of 40 and 150 by Listing Common Multiples The first step to this method of finding the Least Common Multiple of 40 and 150 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, 40 and 150: What are the Multiples of 40? What are the Multiples of 150? Let’s take a look at the first 10 multiples for each of these numbers, 40 and 150: First 10 Multiples of 40: 40, 80, 120, 160, 200, 240, 280, 320, 360, 400 First 10 Multiples of 150: 150, 300, 450, 600, 750, 900, 1050, 1200, 1350, 1500 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 40 and 150 are 600, 1200, 1800. Because 600 is the smallest, it is the least common multiple. The LCM of 40 and 150 is 600. Find the LCM of Other Number Pairs Want more practice? Try some of these other LCM problems: What is the LCM of 42 and 63? What is the LCM of 54 and 11? What is the LCM of 22 and 112? What is the LCM of 1 and 59? What is the LCM of 58 and 37?