LCM of 138, 214, 338, 685, 900
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 138, 214, 338, 685, 900 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, 214, 338, 685, 900. So, keep reading to learn more.
Given numbers are 138,214,338,685,900
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 138,214,338,685,900 is 51281579700.
Find LCM of 138,214,338,685,900 with Prime Factorization
| 2 | 138, 214, 338, 685, 900 |
| 3 | 69, 107, 169, 685, 450 |
| 5 | 23, 107, 169, 685, 150 |
| 23, 107, 169, 137, 30 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 5 x 23 x 107 x 169 x 137 x 30 = 51281579700
Therefore, the lowest common multiple of 138,214,338,685,900 is 51281579700.
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 214 x 338 x 685 x 900 = 6153789564000
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
214 : 1, 2, 107, 214
338 : 1, 2, 13, 26, 169, 338
685 : 1, 5, 137, 685
900 : 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 900
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 138,214,338,685,900, is 1.
Now, the common factors can be found like this.
138:2x 3x 23
214:2x 107
338:2x 13x 13
685:5x 137
900:2x 2x 3x 3x 5x 5
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 3x 5 = 120
Therefore, the value for common factors is 120.
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 = 6153789564000/(1x120)
LCM = 6153789564000/120
LCM = 51281579700
Thus, we can understand that the LCM of 138,214,338,685,900 is 51281579700.
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FAQs on LCM of 138, 214, 338, 685, 900
1. What is the LCM of 138, 214, 338, 685, 900?
Answer: LCM of 138, 214, 338, 685, 900 is 51281579700.
2. How to calculate the LCM of 138, 214, 338, 685, 900?
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, 214, 338, 685, 900.
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}.