LCM of 960, 75, 192
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 960, 75, 192 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 960, 75, 192. So, keep reading to learn more.
Given numbers are 960,75,192
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 960,75,192 is 4800.
Find LCM of 960,75,192 with Prime Factorization
| 2 | 960, 75, 192 |
| 2 | 480, 75, 96 |
| 2 | 240, 75, 48 |
| 2 | 120, 75, 24 |
| 2 | 60, 75, 12 |
| 2 | 30, 75, 6 |
| 3 | 15, 75, 3 |
| 5 | 5, 25, 1 |
| 1, 5, 1 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 1 x 5 x 1 = 4800
Therefore, the lowest common multiple of 960,75,192 is 4800.
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.
960 x 75 x 192 = 13824000
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.
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
75 : 1, 3, 5, 15, 25, 75
192 : 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 960,75,192, is 3.
Now, the common factors can be found like this.
960:2x 2x 2x 2x 2x 2x 3x 5
75:3x 5x 5
192:2x 2x 2x 2x 2x 2x 3
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 2x 2x 3x 5 = 960
Therefore, the value for common factors is 960.
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 = 13824000/(3x960)
LCM = 13824000/2880
LCM = 4800
Thus, we can understand that the LCM of 960,75,192 is 4800.
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FAQs on LCM of 960, 75, 192
1. What is the LCM of 960, 75, 192?
Answer: LCM of 960, 75, 192 is 4800.
2. How to calculate the LCM of 960, 75, 192?
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 960, 75, 192.
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}.