LCM of 920, 217, 735, 314
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 920, 217, 735, 314 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 920, 217, 735, 314. So, keep reading to learn more.
Given numbers are 920,217,735,314
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 920,217,735,314 is 658213080.
Find LCM of 920,217,735,314 with Prime Factorization
| 2 | 920, 217, 735, 314 |
| 5 | 460, 217, 735, 157 |
| 7 | 92, 217, 147, 157 |
| 92, 31, 21, 157 |
Multiply the prime numbers at the bottom and the left side.
2 x 5 x 7 x 92 x 31 x 21 x 157 = 658213080
Therefore, the lowest common multiple of 920,217,735,314 is 658213080.
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.
920 x 217 x 735 x 314 = 46074915600
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.
920 : 1, 2, 4, 5, 8, 10, 20, 23, 40, 46, 92, 115, 184, 230, 460, 920
217 : 1, 7, 31, 217
735 : 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735
314 : 1, 2, 157, 314
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 920,217,735,314, is 1.
Now, the common factors can be found like this.
920:2x 2x 2x 5x 23
217:7x 31
735:3x 5x 7x 7
314:2x 157
From this, we can see that the common factors because they appear for more than two numbers. So, just multiply them all together.
2x 5x 7 = 70
Therefore, the value for common factors is 70.
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 = 46074915600/(1x70)
LCM = 46074915600/70
LCM = 658213080
Thus, we can understand that the LCM of 920,217,735,314 is 658213080.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 920, 217, 735, 314
1. What is the LCM of 920, 217, 735, 314?
Answer: LCM of 920, 217, 735, 314 is 658213080.
2. How to calculate the LCM of 920, 217, 735, 314?
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 920, 217, 735, 314.
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}.