LCM of 189, 678, 396, 390
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 189, 678, 396, 390 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 189, 678, 396, 390. So, keep reading to learn more.
Given numbers are 189,678,396,390
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 189,678,396,390 is 61081020.
Find LCM of 189,678,396,390 with Prime Factorization
| 2 | 189, 678, 396, 390 |
| 3 | 189, 339, 198, 195 |
| 3 | 63, 113, 66, 65 |
| 21, 113, 22, 65 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 3 x 21 x 113 x 22 x 65 = 61081020
Therefore, the lowest common multiple of 189,678,396,390 is 61081020.
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.
189 x 678 x 396 x 390 = 19790250480
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.
189 : 1, 3, 7, 9, 21, 27, 63, 189
678 : 1, 2, 3, 6, 113, 226, 339, 678
396 : 1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 132, 198, 396
390 : 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, 390
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 189,678,396,390, is 3.
Now, the common factors can be found like this.
189:3x 3x 3x 7
678:2x 3x 113
396:2x 2x 3x 3x 11
390:2x 3x 5x 13
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 3x 3x 3 = 108
Therefore, the value for common factors is 108.
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 = 19790250480/(3x108)
LCM = 19790250480/324
LCM = 61081020
Thus, we can understand that the LCM of 189,678,396,390 is 61081020.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 189, 678, 396, 390
1. What is the LCM of 189, 678, 396, 390?
Answer: LCM of 189, 678, 396, 390 is 61081020.
2. How to calculate the LCM of 189, 678, 396, 390?
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 189, 678, 396, 390.
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}.