Loading…
Math Tutor Solution: The LCM of 54 and 105 is 1890
Methods
How to find the LCM of 54 and 105 using Prime Factorization
As your math tutor, I'm here to guide you through this problem! To find the LCM of 54 and 105, 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 54:
And this is the prime factorization of 105:
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, 5, 7
Through this we see that the LCM of 54 and 105 is 1890.
How to Find the LCM of 54 and 105 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 54 and 105 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, 54 and 105:
Let’s take a look at the first 10 multiples for each of these numbers, 54 and 105:
First 10 Multiples of 54: 54, 108, 162, 216, 270, 324, 378, 432, 486, 540
First 10 Multiples of 105: 105, 210, 315, 420, 525, 630, 735, 840, 945, 1050
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 54 and 105 are 1890, 3780, 5670. Because 1890 is the smallest, it is the least common multiple.
The LCM of 54 and 105 is 1890.
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
Math 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