LCM of 314, 765, 398, 414
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 314, 765, 398, 414 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 314, 765, 398, 414. So, keep reading to learn more.
Given numbers are 314,765,398,414
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 314,765,398,414 is 1099441170.
Find LCM of 314,765,398,414 with Prime Factorization
| 2 | 314, 765, 398, 414 |
| 3 | 157, 765, 199, 207 |
| 3 | 157, 255, 199, 69 |
| 157, 85, 199, 23 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 3 x 157 x 85 x 199 x 23 = 1099441170
Therefore, the lowest common multiple of 314,765,398,414 is 1099441170.
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.
314 x 765 x 398 x 414 = 39579882120
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.
314 : 1, 2, 157, 314
765 : 1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255, 765
398 : 1, 2, 199, 398
414 : 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 314,765,398,414, is 1.
Now, the common factors can be found like this.
314:2x 157
765:3x 3x 5x 17
398:2x 199
414:2x 3x 3x 23
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 3 = 36
Therefore, the value for common factors is 36.
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 = 39579882120/(1x36)
LCM = 39579882120/36
LCM = 1099441170
Thus, we can understand that the LCM of 314,765,398,414 is 1099441170.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 314, 765, 398, 414
1. What is the LCM of 314, 765, 398, 414?
Answer: LCM of 314, 765, 398, 414 is 1099441170.
2. How to calculate the LCM of 314, 765, 398, 414?
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 314, 765, 398, 414.
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}.