LCM of 824, 428, 360, 900
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 824, 428, 360, 900 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 824, 428, 360, 900. So, keep reading to learn more.
Given numbers are 824,428,360,900
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 824,428,360,900 is 19837800.
Find LCM of 824,428,360,900 with Prime Factorization
| 2 | 824, 428, 360, 900 |
| 2 | 412, 214, 180, 450 |
| 2 | 206, 107, 90, 225 |
| 3 | 103, 107, 45, 225 |
| 3 | 103, 107, 15, 75 |
| 5 | 103, 107, 5, 25 |
| 103, 107, 1, 5 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 3 x 5 x 103 x 107 x 1 x 5 = 19837800
Therefore, the lowest common multiple of 824,428,360,900 is 19837800.
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.
824 x 428 x 360 x 900 = 114265728000
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.
824 : 1, 2, 4, 8, 103, 206, 412, 824
428 : 1, 2, 4, 107, 214, 428
360 : 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
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
4 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 824,428,360,900, is 4.
Now, the common factors can be found like this.
824:2x 2x 2x 103
428:2x 2x 107
360:2x 2x 2x 3x 3x 5
900:2x 2x 3x 3x 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 3x 5 = 1440
Therefore, the value for common factors is 1440.
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 = 114265728000/(4x1440)
LCM = 114265728000/5760
LCM = 19837800
Thus, we can understand that the LCM of 824,428,360,900 is 19837800.
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FAQs on LCM of 824, 428, 360, 900
1. What is the LCM of 824, 428, 360, 900?
Answer: LCM of 824, 428, 360, 900 is 19837800.
2. How to calculate the LCM of 824, 428, 360, 900?
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 824, 428, 360, 900.
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}.