LCM of 416, 900, 674, 400
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 416, 900, 674, 400 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 416, 900, 674, 400. So, keep reading to learn more.
Given numbers are 416,900,674,400
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 416,900,674,400 is 31543200.
Find LCM of 416,900,674,400 with Prime Factorization
| 2 | 416, 900, 674, 400 |
| 2 | 208, 450, 337, 200 |
| 2 | 104, 225, 337, 100 |
| 2 | 52, 225, 337, 50 |
| 5 | 26, 225, 337, 25 |
| 5 | 26, 45, 337, 5 |
| 26, 9, 337, 1 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 2 x 5 x 5 x 26 x 9 x 337 x 1 = 31543200
Therefore, the lowest common multiple of 416,900,674,400 is 31543200.
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.
416 x 900 x 674 x 400 = 100938240000
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.
416 : 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416
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
674 : 1, 2, 337, 674
400 : 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 416,900,674,400, is 2.
Now, the common factors can be found like this.
416:2x 2x 2x 2x 2x 13
900:2x 2x 3x 3x 5x 5
674:2x 337
400:2x 2x 2x 2x 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 2x 2x 2x 5x 5 = 1600
Therefore, the value for common factors is 1600.
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 = 100938240000/(2x1600)
LCM = 100938240000/3200
LCM = 31543200
Thus, we can understand that the LCM of 416,900,674,400 is 31543200.
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FAQs on LCM of 416, 900, 674, 400
1. What is the LCM of 416, 900, 674, 400?
Answer: LCM of 416, 900, 674, 400 is 31543200.
2. How to calculate the LCM of 416, 900, 674, 400?
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 416, 900, 674, 400.
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}.