LCM of 108, 493, 204, 900
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 108, 493, 204, 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 108, 493, 204, 900. So, keep reading to learn more.
Given numbers are 108,493,204,900
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 108,493,204,900 is 1331100.
Find LCM of 108,493,204,900 with Prime Factorization
| 2 | 108, 493, 204, 900 |
| 2 | 54, 493, 102, 450 |
| 3 | 27, 493, 51, 225 |
| 3 | 9, 493, 17, 75 |
| 17 | 3, 493, 17, 25 |
| 3, 29, 1, 25 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 3 x 17 x 3 x 29 x 1 x 25 = 1331100
Therefore, the lowest common multiple of 108,493,204,900 is 1331100.
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.
108 x 493 x 204 x 900 = 9775598400
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.
108 : 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
493 : 1, 17, 29, 493
204 : 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204
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 108,493,204,900, is 1.
Now, the common factors can be found like this.
108:2x 2x 3x 3x 3
493:17x 29
204:2x 2x 3x 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 2x 3x 3x 3x 17 = 7344
Therefore, the value for common factors is 7344.
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 = 9775598400/(1x7344)
LCM = 9775598400/7344
LCM = 1331100
Thus, we can understand that the LCM of 108,493,204,900 is 1331100.
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FAQs on LCM of 108, 493, 204, 900
1. What is the LCM of 108, 493, 204, 900?
Answer: LCM of 108, 493, 204, 900 is 1331100.
2. How to calculate the LCM of 108, 493, 204, 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 108, 493, 204, 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}.