Solving Equations Using the Least Common Multiple

Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

There are several methods that can be used to solve equations. In this lesson, you'll learn about using the least common multiple method to help you combine and solve for your variable.

Least Common Multiple

You might remember from your fraction days that the least common multiple (LCM), the lowest number that is a multiple of all your given numbers, is a number that can help you combine fractions. For example, to add 1/2 and 3/4, you have to find the least common multiple for the denominator before you could add these two fractions together like this.

  • 1/2 + 3/4 = 2/4 + 3/4 = 5/4

The least common multiple for the denominator here is 4.

Using LCM to Solve Equations

Well, you can use the least common multiple to help you solve your algebraic equations when you need to combine fractions to help you simplify your equations. To do this, follow these steps.

  1. Move all your variable terms to one side of the equation and all your constant terms to the other.
  2. Use the LCM to combine any fraction terms that are like terms.
  3. Continue solving for your variable by using your algebra skills.

Practice Problem 1

Let's take a look at these steps in action now.

Let's solve this equation for the x variable.

solve with lcm

Following the steps, you first move all your variable terms to one side. So pick one side, say the left side. Now move all the constant terms to the other side, the right side. Here is what it looks like.

solve with lcm

Now, in the second step, combine your fractions with the help of the least common multiple. You are combining fractions, so your least common multiple will help you figure out what your denominators need to be before you can simplify this part of your equation.

You have 7 and 2 as denominators, so your least common multiple for these two numbers is 14. So you need to change both fractions so they both have a denominator of 14. Then you can combine them.

solve with lcm

After using the LCM to help you combine fraction terms, continue solving for your variable using your algebra skills.

solve with lcm

And you are done! Your answer is -28.

Practice Problem 2

Let's look at another example and see if you can solve it on your own before reading the answer that follows.

This time, solve this equation for the unknown variable.

solve with lcm

To unlock this lesson you must be a Member.
Create your account

Register to view this lesson

Are you a student or a teacher?

Unlock Your Education

See for yourself why 30 million people use

Become a member and start learning now.
Become a Member  Back
What teachers are saying about
Try it risk-free for 30 days

Earning College Credit

Did you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Create an account to start this course today
Try it risk-free for 30 days!
Create An Account