LCM of 108, 768, 384, 756
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 108, 768, 384, 756 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 108, 768, 384, 756. So, keep reading to learn more.
Given numbers are 108,768,384,756
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 108,768,384,756 is 48384.
Find LCM of 108,768,384,756 with Prime Factorization
| 2 | 108, 768, 384, 756 |
| 2 | 54, 384, 192, 378 |
| 2 | 27, 96, 192, 189 |
| 2 | 27, 48, 96, 189 |
| 2 | 27, 24, 48, 189 |
| 2 | 27, 12, 24, 189 |
| 2 | 27, 6, 12, 189 |
| 3 | 27, 3, 6, 189 |
| 3 | 9, 1, 2, 63 |
| 3 | 3, 1, 2, 21 |
| 1, 1, 2, 7 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 1 x 1 x 2 x 7 = 48384
Therefore, the lowest common multiple of 108,768,384,756 is 48384.
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.
108 x 768 x 384 x 756 = 24078974976
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.
108 : 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
768 : 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768
384 : 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384
756 : 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 42, 54, 63, 84, 108, 126, 189, 252, 378, 756
12 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 108,768,384,756, is 12.
Now, the common factors can be found like this.
108:2x 2x 3x 3x 3
768:2x 2x 2x 2x 2x 2x 2x 2x 3
384:2x 2x 2x 2x 2x 2x 2x 3
756:2x 2x 3x 3x 3x 7
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 2x 2x 2x 3x 3x 3x 3 = 41472
Therefore, the value for common factors is 41472.
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 = 24078974976/(12x41472)
LCM = 24078974976/497664
LCM = 48384
Thus, we can understand that the LCM of 108,768,384,756 is 48384.
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FAQs on LCM of 108, 768, 384, 756
1. What is the LCM of 108, 768, 384, 756?
Answer: LCM of 108, 768, 384, 756 is 48384.
2. How to calculate the LCM of 108, 768, 384, 756?
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 108, 768, 384, 756.
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}.