/*! 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 24 What is the least common multipl... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 24

What is the least common multiple of 6 and 9 ? A. 9 B. 18 C. 36 D. 54

Short Answer

Expert verified
The least common multiple of 6 and 9 is 18.

Step by step solution

01

- List the Prime Factors

List the prime factors of both numbers. For 6: 2 and 3. For 9: 3 and 3.
02

- Identify the Highest Powers

Determine the highest powers of all prime factors present from both numbers. For 6: 2鹿 and 3鹿. For 9: 3虏.
03

- Calculate the LCM

Multiply the highest powers of the prime factors together to find the LCM. The highest power of 2 is 2鹿 (from 6). The highest power of 3 is 3虏 (from 9). Therefore, the LCM is 2鹿 脳 3虏 = 2 脳 9 = 18.

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 factors
Prime factors are the building blocks of a number, breaking it down into smaller prime numbers that multiply together to make the original number. A prime number is a number that has only two distinct positive divisors: one and itself.

To find the prime factors of a given number, you can use the method of division by the smallest prime numbers. For instance, to find the prime factors of 6 and 9:
  • 6 can be divided by 2 to give 3, both 2 and 3 are primes, so the prime factors of 6 are 2 and 3.
  • 9 can be divided by 3 continuously (9 梅 3 = 3, 3 梅 3 = 1), resulting in prime factors of 3 and 3.
Understanding prime factors is essential because every number is a composition of prime factors, and they are used in various calculations such as finding the least common multiple (LCM) and greatest common divisor (GCD).
highest powers
In the context of finding the LCM, the highest powers of prime factors refer to the largest exponent of each prime factor that appears in the prime factorization of the numbers involved. This ensures that the LCM contains all the necessary multiples of these primes.

For instance, when determining the LCM of 6 and 9:
  • For 6, the prime factorization is 2鹿 and 3鹿.
  • For 9, the prime factorization is 3虏.
Among these, the highest power of 2 is 2鹿 (from 6), and the highest power of 3 is 3虏 (from 9).

It's important to consider the highest powers because they ensure that the LCM is the lowest number that is a multiple of both original numbers. Any lower power would fail to cover the requirement for one of the numbers.
calculating LCM
Calculating the least common multiple (LCM) involves combining the highest powers of all prime factors derived from the numbers involved. This method results in the smallest positive integer that is divisible by each of the given numbers.

Here's how you do it for 6 and 9:
  • From the step of identifying the highest powers, we get: the highest power of 2 is 2鹿, and the highest power of 3 is 3虏.
  • To find the LCM, simply multiply these highest powers together: \[LCM = 2^1 \times 3^2 = 2 \times 9 = 18\].
Therefore, the LCM of 6 and 9 is 18. This ensures that 18 is the smallest number that both 6 and 9 can divide into without leaving a remainder.

Finding the LCM is very useful in problems where synchronization of cycles, combining of different periodic events, or finding common denominators in fractions is required.

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

Which situation describes quantities combining to make 0 ? A. An account overdrawn by \(\$ 1367\) receives a payroll deposit of \(\$ 756\) and a tax refund deposit of \(\$ 621\). B. 5 people chip in \(\$ 17\) each to help settle a friend's \(\$ 85\) electricity bill. C. A person contributes \(\$ 15\) to pay for his share of a \(\$ 60\) dinner bill; his 4 companions all generously do the same. D. Oil leaks out of a full 75,000 -gallon tank at the rate of 1500 gallons each day for 7 weeks before someone notices.

Which statement is true? A. \(-3<-7\) B. -3 is to the right of -7 of the number line. C. \(|-3|>|-7|\) D. -3 is to the left of -7 on the number line.

Which point is the reflection of \((2,-5)\) on the \(y\)-axis? A. \((-2,5)\) B. \((5,-2)\) C. \((-5,2)\) D. \((-2,-5)\)

Which of the following is undefined? A. \(\frac{-2+2}{8+(-4)}\) B. \(\frac{5+(-2)}{-7+7}\) C. \(\frac{4-(-1)}{6-3}\) D. \(\frac{-3+(-1)}{4-(-6)}\)

On a number line, where is the number \(-2+(-7) ?\) A. 7 units to the right of -2 B. -7 units to the left of -2 C. -7 units to the right of -2 D. 7 units to the left of -2
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Geometry

Read Explanation

Logic and Functions

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

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.