What is the Least Common Multiple (LCM) of 30 and 84?
If you are searching to find out what the lowest common multiple of 30 and 84 is then you probably figured out you are in the right place! That's exactly what this quick guide is all about. We'll walk you through how to calculate the least common multiple for any numbers you need to check. Keep reading!
First off, if you're in a rush, here's the answer to the question "what is the LCM of 30 and 84?":
LCM(30, 84) = 420
What is the Least Common Multiple?
In simple terms, the LCM is the smallest possible whole number (an integer) that divides evenly into all of the numbers in the set. It's also sometimes called the least common divisor, or LCD.
There are a number of different ways to calculate the GCF of a set of numbers depending how many numbers you have and how large they are.
For smaller numbers you can simply look at the factors or multiples for each number and find the least common multiple of them.
For 30 and 84 those factors look like this:
- Factors for 30: 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, and 420
- Factors for 84: 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, and 420
As you can see when you list out the factors of each number, 420 is the greatest number that 30 and 84 divides into.
As the numbers get larger, or you want to compare multiple numbers at the same time to find the GCF, you can see how listing out all of the factors would become too much. To fix this, you can use prime factors.
List out all of the prime factors for each number:
- Prime Factors for 30: 2, 3, and 5
- Prime Factors for 84: 2, 2, 3, and 7
Now that we have the list of prime factors, we need to list out all of the prime factors as often as they occur for each given number and then multiply them together. In our example, this becomes:
LCM = 2 x 3 x 5 x 7 = 210
Other Ways to Calculate LCM
There are a number of other ways in which you can calculate the least common multiple of numbers, including:
- Prime factorization using exponents
- The cake/ladder method
- The division method
- Using the greatest common factor (GCF)
For the purposes of this tutorial, using factors or prime factors should help you to calculate the answer easily. If you really want to brush up on your math, you can research the other methods and become a full blown LCM expert.
Hopefully you've learned a little math today (but not too much!) and understand how to calculate the LCM of numbers. The next challenge is to pick a couple of new numbers yourself and try to work it out using the above methods.
Not feeling like doing the hard work? No worries! Head back to our LCM calculator instead and let our tool do the hard work for you :)
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"Least Common Multiple of 30 and 84". VisualFractions.com. Accessed on December 5, 2022. http://visualfractions.com/calculator/least-common-multiple/lcm-of-30-and-84/.
"Least Common Multiple of 30 and 84". VisualFractions.com, http://visualfractions.com/calculator/least-common-multiple/lcm-of-30-and-84/. Accessed 5 December, 2022.
Least Common Multiple of 30 and 84. VisualFractions.com. Retrieved from http://visualfractions.com/calculator/least-common-multiple/lcm-of-30-and-84/.
Random List of LCM Examples
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