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Least Common Multiples (LCMs)

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Least Common Multiples (LCMs)

Study Guide

Key Definition

The least common multiple (LCM) of two whole numbers $a$ and $b$ is the smallest number among the common multiples of these numbers.

Important Notes

The LCM is the smallest positive number that is divisible by both numbers
LCM is useful for adding and subtracting fractions with different denominators
To find the LCM, you can list multiples or use the prime factorization method
The LCM is always greater than or equal to the largest number in the set
LCM is often used in solving real-world problems such as scheduling

Mathematical Notation

$\times$ represents multiplication

$\frac{a}{b}$ represents a fraction

$x^2$ means x squared

$\sqrt{x}$ represents the square root of x

Remember to use proper notation when solving problems

Why It Works

The LCM allows you to find a common denominator for fractions and understand patterns in numbers. By listing multiples or using prime factorization, you identify the smallest shared value.

Remember

The LCM is critical for calculations in algebra and arithmetic, ensuring calculations with fractions are accurate.

Quick Reference

LCM of 9 and 12:$36$

LCM of 6 and 8:$24$

Understanding Least Common Multiples (LCMs)

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

To find the LCM of two numbers, list their multiples until you find the smallest one they share. For example, for 4 and 5: multiples of 4 are 4, 8, 12, 16, 20; multiples of 5 are 5, 10, 15, 20. They both share 20, so LCM(4,5) = 20.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the LCM of $4$ and $5$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

You have two friends. One visits every 4 days, and another every 6 days. When will they both visit on the same day again?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Find the LCM of three numbers: $6, 9,$ and $12$. What is the smallest number that all three divide evenly into?

Challenge Quiz

Single Choice Quiz

Advanced

Find the LCM of $14, 20,$ and $28$.

Recap

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Review key concepts and takeaways