LCM of 138, 678, 411, 840
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 138, 678, 411, 840 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 138, 678, 411, 840. So, keep reading to learn more.
Given numbers are 138,678,411,840
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 138,678,411,840 is 299092920.
Find LCM of 138,678,411,840 with Prime Factorization
| 2 | 138, 678, 411, 840 |
| 3 | 69, 339, 411, 420 |
| 23, 113, 137, 140 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 23 x 113 x 137 x 140 = 299092920
Therefore, the lowest common multiple of 138,678,411,840 is 299092920.
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.
138 x 678 x 411 x 840 = 32302035360
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.
138 : 1, 2, 3, 6, 23, 46, 69, 138
678 : 1, 2, 3, 6, 113, 226, 339, 678
411 : 1, 3, 137, 411
840 : 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 138,678,411,840, is 3.
Now, the common factors can be found like this.
138:2x 3x 23
678:2x 3x 113
411:3x 137
840:2x 2x 2x 3x 5x 7
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 3 = 36
Therefore, the value for common factors is 36.
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 = 32302035360/(3x36)
LCM = 32302035360/108
LCM = 299092920
Thus, we can understand that the LCM of 138,678,411,840 is 299092920.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 138, 678, 411, 840
1. What is the LCM of 138, 678, 411, 840?
Answer: LCM of 138, 678, 411, 840 is 299092920.
2. How to calculate the LCM of 138, 678, 411, 840?
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 138, 678, 411, 840.
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}.