Grade 4
  1. Numbers and Place Value  1.1. Understanding Place Value  1.2. Reading and Writing Large Numbers  1.3. Comparing and Ordering Numbers  1.4. Rounding Numbers  1.5. Understanding Odd and Even Numbers  1.6. Number Patterns and Sequences
  2. Addition and Subtraction  2.1. Addition of Large Numbers  2.2. Subtraction of Large Numbers  2.3. Estimation in Addition and Subtraction  2.4. Word Problems on Addition and Subtraction
  3. Multiplication and Division  3.1. Understanding Multiplication  3.2. Multiplying Multi-Digit Numbers  3.3. Understanding Division  3.4. Dividing Multi-Digit Numbers  3.5. Multiplication and Division Facts  3.6. Word Problems on Multiplication and Division
  4. Factors and Multiples  4.1. Understanding Factors  4.2. Finding Common Factors  4.3. Understanding Multiples  4.4. Finding Common Multiples  4.5. Prime and Composite Numbers  4.6. Prime Factorization  4.7. Greatest Common Factor  4.8. Least Common Multiple
  5. Fractions  5.1. Understanding Fractions  5.2. Equivalent Fractions  5.3. Simplifying Fractions  5.4. Comparing and Ordering Fractions  5.5. Addition of Fractions  5.6. Subtraction of Fractions  5.7. Mixed Numbers and Improper Fractions  5.8. Converting Mixed Numbers to Improper Fractions  5.9. Word Problems on Fractions
  6. Decimals  6.1. Understanding Decimals  6.2. Reading and Writing Decimals  6.3. Comparing and Ordering Decimals  6.4. Rounding Decimals  6.5. Addition of Decimals  6.6. Subtraction of Decimals  6.7. Converting Decimals to Fractions  6.8. Converting Fractions to Decimals  6.9. Word Problems on Decimals
  7. Measurement  7.1. Length  7.1.1. Units of Length  7.1.2. Converting Units of Length  7.1.3. Perimeter  7.1.4. Area  7.1.5. Word Problems on Length  7.2. Weight  7.2.1. Units of Weight  7.2.2. Converting Units of Weight  7.2.3. Word Problems on Weight  7.3. Volume and Capacity  7.3.1. Units of Volume  7.3.2. Converting Units of Volume  7.3.3. Estimating Volume and Capacity  7.3.4. Word Problems on Volume and Capacity  7.4. Time  7.4.1. Reading Time  7.4.2. Units of Time  7.4.3. Converting Units of Time  7.4.4. Calculating Elapsed Time  7.4.5. Word Problems on Time
  8. Geometry  8.1. Properties of Shapes  8.1.1. Types of Angles  8.1.2. Types of Triangles  8.1.4. Symmetry  8.1.5. Lines of Symmetry  8.2. Perimeter and Area  8.2.1. Perimeter of Rectangles  8.2.2. Perimeter of Other Shapes  8.2.3. Area of Rectangles  8.2.4. Area of Other Shapes  8.2.5. Area of Irregular Shapes  8.3. Coordinate Geometry  8.3.1. Understanding Coordinates  8.3.2. Plotting Points on a Grid  8.3.3. Identifying Shapes on a Grid
  9. Data and Graphs  9.1. Types of Data  9.2. Organizing Data  9.3. Reading Bar Graphs  9.4. Drawing Bar Graphs  9.5. Line Plots  9.7. Reading and Interpreting Line Graphs  9.8. Word Problems on Graphs
  10. Money  10.1. Understanding Money  10.2. Addition and Subtraction with Money  10.3. Making Change  10.4. Multiplying and Dividing Money  10.5. Word Problems on Money

Grade 4 → Factors and Multiples ↓


Least Common Multiple


In the world of mathematics, understanding concepts such as multiples, least common multiple (LCM) and factors is essential to build a strong foundation. Let's take a deeper look at each of these concepts, focusing specifically on the least common multiple, this What it is, how to find it, and why it's important.

The least common multiple (LCM) is a concept you'll use often as you continue your math journey. Basically, the LCM of two or more numbers is the smallest multiple that those numbers share. But what about LCM? Before delving deeper, let us have a clear understanding of the meaning of multiples.

What is multiple?

The multiple of a number is what you get when you multiply that number by an integer. For example, the multiples of 3 are obtained by multiplying 3 by 1, 2, 3, 4, 5, and so on. So, the multiples of 3 are:

3, 6, 9, 12, 15, 18, 21, ...

Multiplication goes on forever, because you can always multiply by the next whole number, then the next, and so on.

Example of multiples

Let's find the first few multiples of 4:

  • 4 x 1 = 4
  • 4 x 2 = 8
  • 4 x 3 = 12
  • 4 x 4 = 16
  • 4 x 5 = 20

So the multiples of 4 are: 4, 8, 12, 16, 20, ...

Understanding the factors

Before jumping straight into the least common multiple, let us remind ourselves about factors. A factor is a number that divides another number exactly without any remainder. For example, consider the number 12. The numbers that divide 12 exactly are 1, 2, 3, 4, 6 and 12. These numbers are called factors of 12.

It is important to understand factors because they help us when finding the least common multiple.

Example of factor

What are the factors of 15?

  • 1 x 15 = 15
  • 3 x 5 = 15

Therefore, the factors of 15 are: 1, 3, 5, 15

What is least common multiple (LCM)?

Now let's try to understand the least common multiple. The LCM of two or more numbers is the smallest number that is a multiple of both (or all) numbers. LCM is very useful for adding, subtracting or comparing fractions with different denominators. It happens.

Let us understand LCM with a simple example:

Consider two numbers 4 and 5. Let's list their multiples:

  • Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40,...
  • Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50,...

From the list given above you can see that the common multiples of 4 and 5 are 20, 40 and so on. The smallest multiple among these is 20, so the least common multiple of 4 and 5 is 20.

Finding least common multiple

There are a few ways to find the least common multiple:

Method 1: Listing the multiples

This method involves listing the multiples of each number until you find the first common factor.

Example using listing multiples

Find the LCM of 3 and 7:

  • Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, ...
  • Multiples of 7: 7, 14, 21, 28, 35, ...

The first common multiple is 21, so the least common multiple of 3 and 7 is 21.

Although this method is simple, it can be a bit difficult when working with large numbers.

Method 2: Prime factorization

In this method, each number is broken down into its prime factors, then the least common multiple is calculated using these factors.

Examples using prime factorization

Find the LCM of 12 and 18:

  • Prime factors of 12: 2 x 2 x 3 (or 2 2 x 3 1)
  • Prime factors of 18: 2 x 3 x 3 (or 2 1 x 3 2)

For LCM we take the highest power of all prime numbers:

  • 2 2
  • 3 2

So, LCM = 2 2 x 3 2 = 4 x 9 = 36

Method 3: Partition method

This method involves dividing numbers by their common factors until only 1 is left, and then multiplying those factors.

Example using division method

Find the LCM of 8 and 14:

Step 1: Divide both numbers by 2 (a common factor) 
8 ÷ 2 = 4
14 ÷ 2 = 7
Step 2: Multiply the divisors and the remaining quotients
LCM = 2 x 4 x 7 = 56

Use of least common multiple

The LCM is very helpful, especially when working with fractions. If you want to add or subtract fractions with different denominators, finding the LCM of those denominators can help you convert the fractions into equivalent fractions.

Example of using LCM to add fractions

Add 1/3 and 1/4.

Find the LCM of 3 and 4 (which is 12):

  • (1/3) = 4/12 (because 3 x 4 = 12)
  • (1/4) = 3/12 (because 4 x 3 = 12)

Now add: 4/12 + 3/12 = 7/12

This technique makes it easier to perform operations with fractions by using LCM to integrate the denominators.

Importance of least common multiple

Understanding the least common multiple is not just about doing homework or passing exams. It helps with logical thinking and problem solving. Knowing how to find the LCM efficiently can also make many everyday tasks easier, even if they are not math-related.

Being able to recognize where LCM is relevant, and applying it correctly, shows a good grasp of both arithmetic and algebraic fundamentals.

Finally, practicing these methods with different numbers, both small and large, will strengthen your understanding and improve your mathematical skills.

With these methods and examples, you now have a clear understanding of what the least common multiple is, how to find it, and its importance. Keep practicing with different numbers to become proficient at finding the LCM!


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