LCM of 630, 120, 309, 180
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 630, 120, 309, 180 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 630, 120, 309, 180. So, keep reading to learn more.
Given numbers are 630,120,309,180
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 630,120,309,180 is 259560.
Find LCM of 630,120,309,180 with Prime Factorization
| 2 | 630, 120, 309, 180 |
| 2 | 315, 60, 309, 90 |
| 3 | 315, 30, 309, 45 |
| 3 | 105, 10, 103, 15 |
| 5 | 35, 10, 103, 5 |
| 7, 2, 103, 1 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 3 x 5 x 7 x 2 x 103 x 1 = 259560
Therefore, the lowest common multiple of 630,120,309,180 is 259560.
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.
630 x 120 x 309 x 180 = 4204872000
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.
630 : 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 126, 210, 315, 630
120 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
309 : 1, 3, 103, 309
180 : 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 630,120,309,180, is 3.
Now, the common factors can be found like this.
630:2x 3x 3x 5x 7
120:2x 2x 2x 3x 5
309:3x 103
180:2x 2x 3x 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 5x 5 = 5400
Therefore, the value for common factors is 5400.
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 = 4204872000/(3x5400)
LCM = 4204872000/16200
LCM = 259560
Thus, we can understand that the LCM of 630,120,309,180 is 259560.
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FAQs on LCM of 630, 120, 309, 180
1. What is the LCM of 630, 120, 309, 180?
Answer: LCM of 630, 120, 309, 180 is 259560.
2. How to calculate the LCM of 630, 120, 309, 180?
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 630, 120, 309, 180.
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}.