LCM of 413, 900, 380, 400, 120
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 413, 900, 380, 400, 120 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 413, 900, 380, 400, 120. So, keep reading to learn more.
Given numbers are 413,900,380,400,120
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 413,900,380,400,120 is 28249200.
Find LCM of 413,900,380,400,120 with Prime Factorization
| 2 | 413, 900, 380, 400, 120 |
| 2 | 413, 450, 190, 200, 60 |
| 2 | 413, 225, 95, 100, 30 |
| 3 | 413, 225, 95, 50, 15 |
| 5 | 413, 75, 95, 50, 5 |
| 5 | 413, 15, 19, 10, 1 |
| 413, 3, 19, 2, 1 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 5 x 5 x 413 x 3 x 19 x 2 x 1 = 28249200
Therefore, the lowest common multiple of 413,900,380,400,120 is 28249200.
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.
413 x 900 x 380 x 400 x 120 = 6779808000000
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.
413 : 1, 7, 59, 413
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
380 : 1, 2, 4, 5, 10, 19, 20, 38, 76, 95, 190, 380
400 : 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
120 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 413,900,380,400,120, is 1.
Now, the common factors can be found like this.
413:7x 59
900:2x 2x 3x 3x 5x 5
380:2x 2x 5x 19
400:2x 2x 2x 2x 5x 5
120:2x 2x 2x 3x 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 2x 2x 2x 2x 3x 5x 5x 5x 5 = 240000
Therefore, the value for common factors is 240000.
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 = 6779808000000/(1x240000)
LCM = 6779808000000/240000
LCM = 28249200
Thus, we can understand that the LCM of 413,900,380,400,120 is 28249200.
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FAQs on LCM of 413, 900, 380, 400, 120
1. What is the LCM of 413, 900, 380, 400, 120?
Answer: LCM of 413, 900, 380, 400, 120 is 28249200.
2. How to calculate the LCM of 413, 900, 380, 400, 120?
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 413, 900, 380, 400, 120.
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}.