LCM of 105, 210, 312, 206
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 105, 210, 312, 206 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, 210, 312, 206. So, keep reading to learn more.
Given numbers are 105,210,312,206
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 105,210,312,206 is 1124760.
Find LCM of 105,210,312,206 with Prime Factorization
| 2 | 105, 210, 312, 206 |
| 3 | 105, 105, 156, 103 |
| 5 | 35, 35, 52, 103 |
| 7 | 7, 7, 52, 103 |
| 1, 1, 52, 103 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 5 x 7 x 1 x 1 x 52 x 103 = 1124760
Therefore, the lowest common multiple of 105,210,312,206 is 1124760.
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 210 x 312 x 206 = 1417197600
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
210 : 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
312 : 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
206 : 1, 2, 103, 206
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 105,210,312,206, is 1.
Now, the common factors can be found like this.
105:3x 5x 7
210:2x 3x 5x 7
312:2x 2x 2x 3x 13
206:2x 103
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 7 = 1260
Therefore, the value for common factors is 1260.
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 = 1417197600/(1x1260)
LCM = 1417197600/1260
LCM = 1124760
Thus, we can understand that the LCM of 105,210,312,206 is 1124760.
LCM of two or more Numbers Calculation Examples
Here are some samples of LCM of two or more Numbers calculations.
FAQs on LCM of 105, 210, 312, 206
1. What is the LCM of 105, 210, 312, 206?
Answer: LCM of 105, 210, 312, 206 is 1124760.
2. How to calculate the LCM of 105, 210, 312, 206?
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, 210, 312, 206.
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}.