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Math Tutor Solution: The LCM of 105 and 78 is 2730
Methods
How to find the LCM of 105 and 78 using Prime Factorization
As your math tutor, I'm here to guide you through this problem! To find the LCM of 105 and 78, 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 105:
And this is the prime factorization of 78:
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: 3, 5, 7, 2, 13
Through this we see that the LCM of 105 and 78 is 2730.
How to Find the LCM of 105 and 78 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 105 and 78 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, 105 and 78:
Let’s take a look at the first 10 multiples for each of these numbers, 105 and 78:
First 10 Multiples of 105: 105, 210, 315, 420, 525, 630, 735, 840, 945, 1050
First 10 Multiples of 78: 78, 156, 234, 312, 390, 468, 546, 624, 702, 780
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 105 and 78 are 2730, 5460, 8190. Because 2730 is the smallest, it is the least common multiple.
The LCM of 105 and 78 is 2730.
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:
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