Algebra Tutorials!
Saturday 15th of June  
Exponential Decay
Negative Exponents
Multiplying and Dividing Fractions 4
Evaluating Expressions Involving Fractions
The Cartesian Coordinate System
Adding and Subtracting Fractions with Like Denominators
Solving Absolute Value Inequalities
Multiplying Special Polynomials
FOIL Method
Solving Systems of Equations by Graphing
Graphing Compound Inequalities
Solving Quadratic Equations by Completing the Square
Addition Property of Equality
Square Roots
Adding and Subtracting Fractions
The Distance Formula
Graphing Logarithmic Functions
Dividing Mixed Numbers
Evaluating Polynomials
Power of a Product Property of Exponents
Terminology of Algebraic Expressions
Adding and Subtracting Rational Expressions with Identical Denominators
Solving Exponential Equations
Factoring The Difference of 2 Squares
Changing Fractions to Decimals
Solving Linear Equations
Using Patterns to Multiply Two Binomials
Completing the Square
Roots of Complex Numbers
Methods for Solving Quadratic Equations
Conics in Standard Form
Solving Quadratic Equations by Using the Quadratic Formula
Simplifying Fractions 2
Exponential Notation
Exponential Growth
The Cartesian Plane
Graphing Linear Functions
The Slope of a Line
Finding Cube Roots of Large Numbers
Rotating Axes
Common Mistakes With Percents
Solving an Equation That Contains a Square Root
Rational Equations
Properties of Common Logs
Composition of Functions
Using Percent Equations
Solving Inequalities
Properties of Exponents
Graphing Quadratic Functions
Factoring a Polynomial by Finding the GCF
The Rectangular Coordinate System
Adding and Subtracting Fractions
Multiplying and Dividing Rational Expressions
Improper Fractions and Mixed Numbers
Properties of Exponents
Complex Solutions of Quadratic Equations
Solving Nonlinear Equations by Factoring
Solving Quadratic Equations by Factoring
Least Common Multiples
Solving Exponential Equations
Solving Linear Equations
Multiplication Property of Equality
Multiplying Mixed Numbers
Multiplying Fractions
Reducing a Rational Expression to Lowest Terms
Literal Numbers
Factoring Trinomials
Logarithmic Functions
Adding Fractions with Unlike Denominators
Simplifying Square Roots
Adding Fractions
Equations Quadratic in Form
Dividing Rational Expressions
Slopes of Parallel Lines
Simplifying Cube Roots That Contain Variables
Functions and Graphs
Complex Numbers
Multiplying and Dividing Fractions 1
Composition of Functions
Intercepts of a Line
Multiplying Two Numbers with the same Tens Digit and whose Ones Digits add up to 10
Factoring Trinomials
Exponents and Polynomials
Decimals and their Equivalent Fractions
Negative Integer Exponents
Adding and Subtracting Mixed Numbers
Solving Quadratic Equations
Theorem of Pythagoras
Equations 1
Subtracting Fractions
Solving Quadratic Equations by Graphing
Evaluating Polynomials
Angles and Degree Measure
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Least Common Multiples

To add fractions, we need to change the denominators to the least common multiple.

In a multiplication problem, the product (result of multiplication) is also called a multiple of the numbers or factors.



What is the least common multiple of 6 and 9?

Multiples of 6 are: 6, 12, 18, 24, 30, 36, 42, 48, 54, ...

Multiples of 9 are: 9, 18, 27, 36, 45, 54, 63, ...

The numbers in bold are common multiples of 6 and 9.

The least (or lowest or smallest) common multiple of 6 and 9 is 18.

  • We do not call “zero” a multiple of any other number! So the least common multiple of two numbers is never 0. The product is zero if any of the factors are zero.
  • The letters LCM are often used for the term Least Common Multiple.



What is the least common multiple of 12 and 24?

Multiples of 12 are: 12, 24, 36, 48, 60, 72, …

Multiples of 24 are: 24, 48, 72, …

The answer is easy of one number is a multiple of another. The least common multiple is 24.


Do any two numbers always have a common multiple? Yes. The product of the numbers is a common multiple. It may or may not be the least common multiple.

By the way, if two numbers are both prime, then their product is always the least common multiple.

To add or subtract fractions, we need to change them so they have common denominators. Any common multiple will work, but the least common multiple will give you the smallest (and easiest) numbers to work with.



Change this problem to use the least common denominator:

Multiples of 6 are: 6, 12, 18, 24

Multiples of 8 are: 8, 16, 24

The least common multiple is 24, so now convert the fractions.


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