LCM of 284, 540, 320, 123, 440
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 284, 540, 320, 123, 440 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 284, 540, 320, 123, 440. So, keep reading to learn more.
Given numbers are 284,540,320,123,440
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 284,540,320,123,440 is 276661440.
Find LCM of 284,540,320,123,440 with Prime Factorization
| 2 | 284, 540, 320, 123, 440 |
| 2 | 142, 270, 160, 123, 220 |
| 2 | 71, 135, 80, 123, 110 |
| 3 | 71, 135, 40, 123, 55 |
| 5 | 71, 45, 40, 41, 55 |
| 71, 9, 8, 41, 11 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 5 x 71 x 9 x 8 x 41 x 11 = 276661440
Therefore, the lowest common multiple of 284,540,320,123,440 is 276661440.
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.
284 x 540 x 320 x 123 x 440 = 2655949824000
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.
284 : 1, 2, 4, 71, 142, 284
540 : 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540
320 : 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 320
123 : 1, 3, 41, 123
440 : 1, 2, 4, 5, 8, 10, 11, 20, 22, 40, 44, 55, 88, 110, 220, 440
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 284,540,320,123,440, is 1.
Now, the common factors can be found like this.
284:2x 2x 71
540:2x 2x 3x 3x 3x 5
320:2x 2x 2x 2x 2x 2x 5
123:3x 41
440:2x 2x 2x 5x 11
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 5x 5 = 9600
Therefore, the value for common factors is 9600.
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 = 2655949824000/(1x9600)
LCM = 2655949824000/9600
LCM = 276661440
Thus, we can understand that the LCM of 284,540,320,123,440 is 276661440.
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FAQs on LCM of 284, 540, 320, 123, 440
1. What is the LCM of 284, 540, 320, 123, 440?
Answer: LCM of 284, 540, 320, 123, 440 is 276661440.
2. How to calculate the LCM of 284, 540, 320, 123, 440?
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 284, 540, 320, 123, 440.
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}.