/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 21 Find the LCM of each set of numb... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 21

Find the LCM of each set of numbers. $$ 2,3,5 $$

Short Answer

Expert verified
LCM = 30

Step by step solution

01

- Prime Factorization

Identify the prime factors of each number. For the given set: - The prime factors of 2 are simply 2.- The prime factors of 3 are simply 3.- The prime factors of 5 are simply 5.
02

- List All Prime Factors

List all the prime factors, choosing the highest power of each prime factor present in any of the numbers. - From 2, we get 2.- From 3, we get 3.- From 5, we get 5.
03

- Multiply Prime Factors

Multiply these prime factors to find the Least Common Multiple (LCM): \[ LCM = 2 \times 3 \times 5 = 30 \]

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

prime factorization
Prime factorization is the process of breaking down a number into its basic building blocks - prime numbers. Prime numbers are numbers that have only two distinct positive divisors: 1 and the number itself. For example, the prime factors of 2, 3, and 5 are simply 2, 3, and 5 respectively since each number is a prime number itself. This concept is essential when calculating the Least Common Multiple (LCM), as it helps in identifying the fundamental factors that make up each number.
multiplication of prime factors
Once the prime factors of each number are identified, the next step is to list them. For the set of numbers given (2, 3, and 5), this process results in identifying 2, 3, and 5. The key point here is to include the highest power of each prime factor present. In this example, since 2, 3, and 5 are the only factors and all exist as their highest power (which is 1), we simply list each of them.
Next, we multiply these prime factors to get the LCM. It's important to multiply correctly, ensuring all prime factors are represented in the final product.
LCM calculation
Next, we calculate the LCM (Least Common Multiple). The LCM of a set of numbers is the smallest multiple that is exactly divisible by each number in the set.
Here is how it鈥檚 done for our example set (2, 3, 5). We first list all prime factors, taking the highest power of each:
  • From 2, we get 2.
  • From 3, we get 3.
  • From 5, we get 5.

To find the LCM, we multiply these prime factors together: \[ LCM = 2 \times 3 \times 5 = 30 \]
So, the LCM of 2, 3, and 5 is 30. This means 30 is the smallest number that all three original numbers (2, 3, and 5) can divide into without leaving a remainder. This method ensures that the LCM calculation is accurate and straightforward.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Simplify. $$ \frac{\frac{3}{5}-\frac{1}{2}}{\frac{1}{2}-\frac{2}{5}} $$

Subtract and simplify. $$ \frac{3}{4}-\frac{1}{8} $$

Estimate each of the following as \(0, \frac{1}{2},\) or 1 . $$ \frac{5}{9} $$

Vertical Leaps. Eight-year-old Zachary registered vertical leaps of \(12 \frac{3}{4}\) in. \(13 \frac{3}{4}\) in., \(13 \frac{1}{2}\) in., and 14 in. Find ais average vertical leap.

Simplify. $$ \frac{3}{4}-\frac{2}{3} \cdot\left(\frac{1}{2}+\frac{2}{5}\right) $$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.