LCM of 831, 912, 900, 105
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 831, 912, 900, 105 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 831, 912, 900, 105. So, keep reading to learn more.
Given numbers are 831,912,900,105
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 831,912,900,105 is 132627600.
Find LCM of 831,912,900,105 with Prime Factorization
| 2 | 831, 912, 900, 105 |
| 2 | 831, 456, 450, 105 |
| 3 | 831, 228, 225, 105 |
| 5 | 277, 76, 75, 35 |
| 277, 76, 15, 7 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 5 x 277 x 76 x 15 x 7 = 132627600
Therefore, the lowest common multiple of 831,912,900,105 is 132627600.
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.
831 x 912 x 900 x 105 = 71618904000
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.
831 : 1, 3, 277, 831
912 : 1, 2, 3, 4, 6, 8, 12, 16, 19, 24, 38, 48, 57, 76, 114, 152, 228, 304, 456, 912
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
105 : 1, 3, 5, 7, 15, 21, 35, 105
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 831,912,900,105, is 3.
Now, the common factors can be found like this.
831:3x 277
912:2x 2x 2x 2x 3x 19
900:2x 2x 3x 3x 5x 5
105:3x 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 3x 5 = 180
Therefore, the value for common factors is 180.
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 = 71618904000/(3x180)
LCM = 71618904000/540
LCM = 132627600
Thus, we can understand that the LCM of 831,912,900,105 is 132627600.
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FAQs on LCM of 831, 912, 900, 105
1. What is the LCM of 831, 912, 900, 105?
Answer: LCM of 831, 912, 900, 105 is 132627600.
2. How to calculate the LCM of 831, 912, 900, 105?
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 831, 912, 900, 105.
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}.