LCM of 840, 765, 900, 905
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 840, 765, 900, 905 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, 765, 900, 905. So, keep reading to learn more.
Given numbers are 840,765,900,905
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 840,765,900,905 is 38770200.
Find LCM of 840,765,900,905 with Prime Factorization
| 2 | 840, 765, 900, 905 |
| 2 | 420, 765, 450, 905 |
| 3 | 210, 765, 225, 905 |
| 3 | 70, 255, 75, 905 |
| 5 | 70, 85, 25, 905 |
| 14, 17, 5, 181 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 3 x 5 x 14 x 17 x 5 x 181 = 38770200
Therefore, the lowest common multiple of 840,765,900,905 is 38770200.
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 765 x 900 x 905 = 523397700000
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
765 : 1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255, 765
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
905 : 1, 5, 181, 905
5 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 840,765,900,905, is 5.
Now, the common factors can be found like this.
840:2x 2x 2x 3x 5x 7
765:3x 3x 5x 17
900:2x 2x 3x 3x 5x 5
905:5x 181
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 3x 5x 5 = 2700
Therefore, the value for common factors is 2700.
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 = 523397700000/(5x2700)
LCM = 523397700000/13500
LCM = 38770200
Thus, we can understand that the LCM of 840,765,900,905 is 38770200.
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FAQs on LCM of 840, 765, 900, 905
1. What is the LCM of 840, 765, 900, 905?
Answer: LCM of 840, 765, 900, 905 is 38770200.
2. How to calculate the LCM of 840, 765, 900, 905?
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, 765, 900, 905.
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}.