LCM of 684, 705, 960
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 684, 705, 960 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 684, 705, 960. So, keep reading to learn more.
Given numbers are 684,705,960
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 684,705,960 is 2571840.
Find LCM of 684,705,960 with Prime Factorization
| 2 | 684, 705, 960 |
| 2 | 342, 705, 480 |
| 3 | 171, 705, 240 |
| 5 | 57, 235, 80 |
| 57, 47, 16 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 5 x 57 x 47 x 16 = 2571840
Therefore, the lowest common multiple of 684,705,960 is 2571840.
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.
684 x 705 x 960 = 462931200
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.
684 : 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684
705 : 1, 3, 5, 15, 47, 141, 235, 705
960 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 684,705,960, is 3.
Now, the common factors can be found like this.
684:2x 2x 3x 3x 19
705:3x 5x 47
960:2x 2x 2x 2x 2x 2x 3x 5
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 5 = 60
Therefore, the value for common factors is 60.
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 = 462931200/(3x60)
LCM = 462931200/180
LCM = 2571840
Thus, we can understand that the LCM of 684,705,960 is 2571840.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 684, 705, 960
1. What is the LCM of 684, 705, 960?
Answer: LCM of 684, 705, 960 is 2571840.
2. How to calculate the LCM of 684, 705, 960?
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 684, 705, 960.
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}.