LCM of 705, 288, 517, 314
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 705, 288, 517, 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 705, 288, 517, 314. So, keep reading to learn more.
Given numbers are 705,288,517,314
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 705,288,517,314 is 116883360.
Find LCM of 705,288,517,314 with Prime Factorization
| 2 | 705, 288, 517, 314 |
| 3 | 705, 144, 517, 157 |
| 47 | 235, 48, 517, 157 |
| 5, 48, 11, 157 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 47 x 5 x 48 x 11 x 157 = 116883360
Therefore, the lowest common multiple of 705,288,517,314 is 116883360.
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.
705 x 288 x 517 x 314 = 32961107520
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.
705 : 1, 3, 5, 15, 47, 141, 235, 705
288 : 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288
517 : 1, 11, 47, 517
314 : 1, 2, 157, 314
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 705,288,517,314, is 1.
Now, the common factors can be found like this.
705:3x 5x 47
288:2x 2x 2x 2x 2x 3x 3
517:11x 47
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 3x 47 = 282
Therefore, the value for common factors is 282.
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 = 32961107520/(1x282)
LCM = 32961107520/282
LCM = 116883360
Thus, we can understand that the LCM of 705,288,517,314 is 116883360.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 705, 288, 517, 314
1. What is the LCM of 705, 288, 517, 314?
Answer: LCM of 705, 288, 517, 314 is 116883360.
2. How to calculate the LCM of 705, 288, 517, 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 705, 288, 517, 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}.