LCM of 396, 900, 288
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 396, 900, 288 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 396, 900, 288. So, keep reading to learn more.
Given numbers are 396,900,288
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 396,900,288 is 79200.
Find LCM of 396,900,288 with Prime Factorization
| 2 | 396, 900, 288 |
| 2 | 198, 450, 144 |
| 3 | 99, 225, 72 |
| 3 | 33, 75, 24 |
| 11, 25, 8 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 3 x 11 x 25 x 8 = 79200
Therefore, the lowest common multiple of 396,900,288 is 79200.
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.
396 x 900 x 288 = 102643200
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.
396 : 1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 132, 198, 396
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
288 : 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288
36 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 396,900,288, is 36.
Now, the common factors can be found like this.
396:2x 2x 3x 3x 11
900:2x 2x 3x 3x 5x 5
288:2x 2x 2x 2x 2x 3x 3
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 3 = 36
Therefore, the value for common factors is 36.
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 = 102643200/(36x36)
LCM = 102643200/1296
LCM = 79200
Thus, we can understand that the LCM of 396,900,288 is 79200.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 396, 900, 288
1. What is the LCM of 396, 900, 288?
Answer: LCM of 396, 900, 288 is 79200.
2. How to calculate the LCM of 396, 900, 288?
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 396, 900, 288.
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}.