LCM of 460, 408, 978, 800
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 460, 408, 978, 800 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 460, 408, 978, 800. So, keep reading to learn more.
Given numbers are 460,408,978,800
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 460,408,978,800 is 152959200.
Find LCM of 460,408,978,800 with Prime Factorization
| 2 | 460, 408, 978, 800 |
| 2 | 230, 204, 489, 400 |
| 2 | 115, 102, 489, 200 |
| 3 | 115, 51, 489, 100 |
| 5 | 115, 17, 163, 100 |
| 23, 17, 163, 20 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 5 x 23 x 17 x 163 x 20 = 152959200
Therefore, the lowest common multiple of 460,408,978,800 is 152959200.
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.
460 x 408 x 978 x 800 = 146840832000
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.
460 : 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460
408 : 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408
978 : 1, 2, 3, 6, 163, 326, 489, 978
800 : 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400, 800
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 460,408,978,800, is 2.
Now, the common factors can be found like this.
460:2x 2x 5x 23
408:2x 2x 2x 3x 17
978:2x 3x 163
800:2x 2x 2x 2x 2x 5x 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 2x 2x 2x 3x 5 = 480
Therefore, the value for common factors is 480.
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 = 146840832000/(2x480)
LCM = 146840832000/960
LCM = 152959200
Thus, we can understand that the LCM of 460,408,978,800 is 152959200.
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FAQs on LCM of 460, 408, 978, 800
1. What is the LCM of 460, 408, 978, 800?
Answer: LCM of 460, 408, 978, 800 is 152959200.
2. How to calculate the LCM of 460, 408, 978, 800?
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 460, 408, 978, 800.
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}.