LCM of 207, 288, 675, 120
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 207, 288, 675, 120 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 207, 288, 675, 120. So, keep reading to learn more.
Given numbers are 207,288,675,120
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 207,288,675,120 is 496800.
Find LCM of 207,288,675,120 with Prime Factorization
| 2 | 207, 288, 675, 120 |
| 2 | 207, 144, 675, 60 |
| 2 | 207, 72, 675, 30 |
| 3 | 207, 36, 675, 15 |
| 3 | 69, 12, 225, 5 |
| 5 | 23, 4, 75, 5 |
| 23, 4, 15, 1 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 3 x 5 x 23 x 4 x 15 x 1 = 496800
Therefore, the lowest common multiple of 207,288,675,120 is 496800.
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.
207 x 288 x 675 x 120 = 4828896000
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.
207 : 1, 3, 9, 23, 69, 207
288 : 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288
675 : 1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225, 675
120 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 207,288,675,120, is 3.
Now, the common factors can be found like this.
207:3x 3x 23
288:2x 2x 2x 2x 2x 3x 3
675:3x 3x 3x 5x 5
120:2x 2x 2x 3x 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 3x 3x 5 = 3240
Therefore, the value for common factors is 3240.
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 = 4828896000/(3x3240)
LCM = 4828896000/9720
LCM = 496800
Thus, we can understand that the LCM of 207,288,675,120 is 496800.
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FAQs on LCM of 207, 288, 675, 120
1. What is the LCM of 207, 288, 675, 120?
Answer: LCM of 207, 288, 675, 120 is 496800.
2. How to calculate the LCM of 207, 288, 675, 120?
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 207, 288, 675, 120.
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}.