Loading…
Math Tutor Solution: The LCM of 138 and 106 is 7314
Methods
How to find the LCM of 138 and 106 using Prime Factorization
As your math tutor, I'm here to guide you through this problem! To find the LCM of 138 and 106, one effective method is comparing their prime factorizations. Start by breaking each number down into its prime factors. Follow these steps to determine the prime factorization of each number:
Here is the prime factorization of 138:
And this is the prime factorization of 106:
When you compare the prime factorization of these two numbers, you want to look for the highest power that each prime factor is raised to. In this case, there are these prime factors to consider: 2, 3, 23, 53
Through this we see that the LCM of 138 and 106 is 7314.
How to Find the LCM of 138 and 106 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 138 and 106 is to begin to list a few multiples for each number. If you need a refresher on how to find the multiples of these numbers, you can see the walkthroughs in the links below for each number.
Let’s take a look at the multiples for each of these numbers, 138 and 106:
Let’s take a look at the first 10 multiples for each of these numbers, 138 and 106:
First 10 Multiples of 138: 138, 276, 414, 552, 690, 828, 966, 1104, 1242, 1380
First 10 Multiples of 106: 106, 212, 318, 424, 530, 636, 742, 848, 954, 1060
You can continue to list out the multiples of these numbers as long as needed to find a match. Once you do find a match, or several matches, the smallest of these matches would be the Least Common Multiple. For instance, the first matching multiple(s) of 138 and 106 are 7314, 14628, 21942. Because 7314 is the smallest, it is the least common multiple.
The LCM of 138 and 106 is 7314.
Math Tutor Suggests: Find the LCM of Other Number Pairs
Want more practice? As a math tutor, I encourage you to try some of these other LCM problems:
Download FREE Math Resources
Take advantage of our free downloadable resources and study materials for at-home learning.
8 Math Hacks and Tricks to Turn Your 'Okay' Math Student Into a Math Champion!
One thing we teach our students at Thinkster is that there are multiple ways to solve a math problem. This helps our students learn to think flexibly and non-linearly.
Get PDF
How to Make Sure Your Child is Highly Successful and Becomes a Millionaire
As a parent, you hope your child is extremely successful and likely become the next Gates, Zuckerberg, or Meg Whitman. To set your child on the right path, there are many skills and traits that you can start building and nurturing now. Doing so plants the seeds for future success.
Get PDFMath Tutoring to Boost Your Child’s Math Skills & Scores by 90% in Just 3 Months – Guaranteed!
Does your child struggle with math homework or understanding tricky math concepts? Do they do okay in math, but express excitement to learn new material or advanced math?
A Thinkster Math tutor provides one-to-one support to help elementary, middle school, and high school students build confidence and master math subjects like K-8 math, pre-algebra, algebra, geometry, calculus, and more.
Our expert math tutors customize math lessons to your child’s unique needs, making learning math fun and effective. We help students improve grades, develop strong critical thinking skills through solving word problems, excel in standardized tests, and develop strong problem-solving skills.
Our expert math tutors are ready to help make your child a champion and develop strong math mastery! Sign up for our 7-day free trial and get the best math tutor for your child today!
Start 7-Day Free Trial