LCM of 314, 678, 576, 144
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 314, 678, 576, 144 with the LCM of Two or More Numbers Calculator. Here we are teaching you two different methods through which you can calculate the LCM of 314, 678, 576, 144. So, keep reading to learn more.
Given numbers are 314,678,576,144
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 314,678,576,144 is 10218816.
Find LCM of 314,678,576,144 with Prime Factorization
| 2 | 314, 678, 576, 144 |
| 2 | 157, 339, 288, 72 |
| 2 | 157, 339, 144, 36 |
| 2 | 157, 339, 72, 18 |
| 3 | 157, 339, 36, 9 |
| 3 | 157, 113, 12, 3 |
| 157, 113, 4, 1 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 2 x 3 x 3 x 157 x 113 x 4 x 1 = 10218816
Therefore, the lowest common multiple of 314,678,576,144 is 10218816.
LCM formula is LCM(a1, a2, an) = (a1 x a2 x an)/{GCF(a1 x a2 x an) x common factors}
Firstly, we have to find the product of all the numbers.
314 x 678 x 576 x 144 = 17658114048
Then, let us find the GCF of these five numbers. To do so, we have to list down the factors for each number and choose the highest factor that is in all of the lists.
314 : 1, 2, 157, 314
678 : 1, 2, 3, 6, 113, 226, 339, 678
576 : 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 144, 192, 288, 576
144 : 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 314,678,576,144, is 2.
Now, the common factors can be found like this.
314:2x 157
678:2x 3x 113
576:2x 2x 2x 2x 2x 2x 3x 3
144:2x 2x 2x 2x 3x 3
From this, we can see that the common factors because they appear for more than two numbers. So, just multiply them all together.
2x 2x 2x 2x 2x 3x 3x 3 = 864
Therefore, the value for common factors is 864.
Now that we have all the elements of the formula, we can plug them in to calculate the LCM.
LCM(a1, a2, an) = (a1 x a2 x an)/{GCF(a1 x a2 x an) x common factors}
LCM = 17658114048/(2x864)
LCM = 17658114048/1728
LCM = 10218816
Thus, we can understand that the LCM of 314,678,576,144 is 10218816.
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FAQs on LCM of 314, 678, 576, 144
1. What is the LCM of 314, 678, 576, 144?
Answer: LCM of 314, 678, 576, 144 is 10218816.
2. How to calculate the LCM of 314, 678, 576, 144?
The LCM can be found using two methods. You can either use the LCM formula or the prime factorization method to calculate the LCM of 314, 678, 576, 144.
3. What is the LCM formula?
The LCM formula is LCM(a1, a2, an) = (a1 x a2 x an)/{GCF(a1 x a2 x an) x common factors}.