LCM of 105, 825, 180, 312
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 105, 825, 180, 312 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, 825, 180, 312. So, keep reading to learn more.
Given numbers are 105,825,180,312
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 105,825,180,312 is 1801800.
Find LCM of 105,825,180,312 with Prime Factorization
| 2 | 105, 825, 180, 312 |
| 2 | 105, 825, 90, 156 |
| 3 | 105, 825, 45, 78 |
| 5 | 35, 275, 15, 26 |
| 7, 55, 3, 26 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 5 x 7 x 55 x 3 x 26 = 1801800
Therefore, the lowest common multiple of 105,825,180,312 is 1801800.
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 825 x 180 x 312 = 4864860000
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
825 : 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825
180 : 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
312 : 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 105,825,180,312, is 3.
Now, the common factors can be found like this.
105:3x 5x 7
825:3x 5x 5x 11
180:2x 2x 3x 3x 5
312:2x 2x 2x 3x 13
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 3x 5x 5 = 900
Therefore, the value for common factors is 900.
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 = 4864860000/(3x900)
LCM = 4864860000/2700
LCM = 1801800
Thus, we can understand that the LCM of 105,825,180,312 is 1801800.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 105, 825, 180, 312
1. What is the LCM of 105, 825, 180, 312?
Answer: LCM of 105, 825, 180, 312 is 1801800.
2. How to calculate the LCM of 105, 825, 180, 312?
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, 825, 180, 312.
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}.