LCM of 678, 144, 384
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 678, 144, 384 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 678, 144, 384. So, keep reading to learn more.
Given numbers are 678,144,384
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 678,144,384 is 130176.
Find LCM of 678,144,384 with Prime Factorization
| 2 | 678, 144, 384 |
| 2 | 339, 72, 192 |
| 2 | 339, 36, 96 |
| 2 | 339, 18, 48 |
| 3 | 339, 9, 24 |
| 113, 3, 8 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 2 x 3 x 113 x 3 x 8 = 130176
Therefore, the lowest common multiple of 678,144,384 is 130176.
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.
678 x 144 x 384 = 37490688
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.
678 : 1, 2, 3, 6, 113, 226, 339, 678
144 : 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
384 : 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384
6 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 678,144,384, is 6.
Now, the common factors can be found like this.
678:2x 3x 113
144:2x 2x 2x 2x 3x 3
384:2x 2x 2x 2x 2x 2x 2x 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 3 = 48
Therefore, the value for common factors is 48.
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 = 37490688/(6x48)
LCM = 37490688/288
LCM = 130176
Thus, we can understand that the LCM of 678,144,384 is 130176.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 678, 144, 384
1. What is the LCM of 678, 144, 384?
Answer: LCM of 678, 144, 384 is 130176.
2. How to calculate the LCM of 678, 144, 384?
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 678, 144, 384.
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}.