LCM of 105, 724, 510, 900
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 105, 724, 510, 900 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 105, 724, 510, 900. So, keep reading to learn more.
Given numbers are 105,724,510,900
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 105,724,510,900 is 19385100.
Find LCM of 105,724,510,900 with Prime Factorization
| 2 | 105, 724, 510, 900 |
| 2 | 105, 362, 255, 450 |
| 3 | 105, 181, 255, 225 |
| 5 | 35, 181, 85, 75 |
| 7, 181, 17, 15 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 5 x 7 x 181 x 17 x 15 = 19385100
Therefore, the lowest common multiple of 105,724,510,900 is 19385100.
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.
105 x 724 x 510 x 900 = 34893180000
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.
105 : 1, 3, 5, 7, 15, 21, 35, 105
724 : 1, 2, 4, 181, 362, 724
510 : 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, 510
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
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 105,724,510,900, is 1.
Now, the common factors can be found like this.
105:3x 5x 7
724:2x 2x 181
510:2x 3x 5x 17
900:2x 2x 3x 3x 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 3x 3x 5x 5 = 1800
Therefore, the value for common factors is 1800.
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 = 34893180000/(1x1800)
LCM = 34893180000/1800
LCM = 19385100
Thus, we can understand that the LCM of 105,724,510,900 is 19385100.
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FAQs on LCM of 105, 724, 510, 900
1. What is the LCM of 105, 724, 510, 900?
Answer: LCM of 105, 724, 510, 900 is 19385100.
2. How to calculate the LCM of 105, 724, 510, 900?
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 105, 724, 510, 900.
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}.