LCM of 840, 900, 825
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 840, 900, 825 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 840, 900, 825. So, keep reading to learn more.
Given numbers are 840,900,825
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 840,900,825 is 138600.
Find LCM of 840,900,825 with Prime Factorization
| 2 | 840, 900, 825 |
| 2 | 420, 450, 825 |
| 3 | 210, 225, 825 |
| 5 | 70, 75, 275 |
| 5 | 14, 15, 55 |
| 14, 3, 11 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 5 x 5 x 14 x 3 x 11 = 138600
Therefore, the lowest common multiple of 840,900,825 is 138600.
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.
840 x 900 x 825 = 623700000
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.
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
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
825 : 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825
15 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 840,900,825, is 15.
Now, the common factors can be found like this.
840:2x 2x 2x 3x 5x 7
900:2x 2x 3x 3x 5x 5
825:3x 5x 5x 11
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 5x 5 = 300
Therefore, the value for common factors is 300.
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 = 623700000/(15x300)
LCM = 623700000/4500
LCM = 138600
Thus, we can understand that the LCM of 840,900,825 is 138600.
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FAQs on LCM of 840, 900, 825
1. What is the LCM of 840, 900, 825?
Answer: LCM of 840, 900, 825 is 138600.
2. How to calculate the LCM of 840, 900, 825?
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 840, 900, 825.
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}.