LCM of 312, 412, 340, 715
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 312, 412, 340, 715 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 312, 412, 340, 715. So, keep reading to learn more.
Given numbers are 312,412,340,715
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 312,412,340,715 is 30047160.
Find LCM of 312,412,340,715 with Prime Factorization
| 2 | 312, 412, 340, 715 |
| 2 | 156, 206, 170, 715 |
| 5 | 78, 103, 85, 715 |
| 13 | 78, 103, 17, 143 |
| 6, 103, 17, 11 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 5 x 13 x 6 x 103 x 17 x 11 = 30047160
Therefore, the lowest common multiple of 312,412,340,715 is 30047160.
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.
312 x 412 x 340 x 715 = 31249046400
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.
312 : 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
412 : 1, 2, 4, 103, 206, 412
340 : 1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 170, 340
715 : 1, 5, 11, 13, 55, 65, 143, 715
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 312,412,340,715, is 1.
Now, the common factors can be found like this.
312:2x 2x 2x 3x 13
412:2x 2x 103
340:2x 2x 5x 17
715:5x 11x 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 2x 2x 5x 13 = 1040
Therefore, the value for common factors is 1040.
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 = 31249046400/(1x1040)
LCM = 31249046400/1040
LCM = 30047160
Thus, we can understand that the LCM of 312,412,340,715 is 30047160.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 312, 412, 340, 715
1. What is the LCM of 312, 412, 340, 715?
Answer: LCM of 312, 412, 340, 715 is 30047160.
2. How to calculate the LCM of 312, 412, 340, 715?
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 312, 412, 340, 715.
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}.