LCM of 104, 240, 900, 768
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 104, 240, 900, 768 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 104, 240, 900, 768. So, keep reading to learn more.
Given numbers are 104,240,900,768
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 104,240,900,768 is 748800.
Find LCM of 104,240,900,768 with Prime Factorization
| 2 | 104, 240, 900, 768 |
| 2 | 52, 120, 450, 384 |
| 2 | 26, 60, 225, 192 |
| 2 | 13, 30, 225, 96 |
| 3 | 13, 15, 225, 48 |
| 5 | 13, 5, 75, 16 |
| 13, 1, 15, 16 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 2 x 3 x 5 x 13 x 1 x 15 x 16 = 748800
Therefore, the lowest common multiple of 104,240,900,768 is 748800.
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.
104 x 240 x 900 x 768 = 17252352000
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.
104 : 1, 2, 4, 8, 13, 26, 52, 104
240 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240
900 : 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 900
768 : 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768
4 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 104,240,900,768, is 4.
Now, the common factors can be found like this.
104:2x 2x 2x 13
240:2x 2x 2x 2x 3x 5
900:2x 2x 3x 3x 5x 5
768:2x 2x 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 2x 3x 3x 5 = 5760
Therefore, the value for common factors is 5760.
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 = 17252352000/(4x5760)
LCM = 17252352000/23040
LCM = 748800
Thus, we can understand that the LCM of 104,240,900,768 is 748800.
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FAQs on LCM of 104, 240, 900, 768
1. What is the LCM of 104, 240, 900, 768?
Answer: LCM of 104, 240, 900, 768 is 748800.
2. How to calculate the LCM of 104, 240, 900, 768?
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 104, 240, 900, 768.
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}.