LCM of 997, 240, 400, 312
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 997, 240, 400, 312 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 997, 240, 400, 312. So, keep reading to learn more.
Given numbers are 997,240,400,312
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 997,240,400,312 is 15553200.
Find LCM of 997,240,400,312 with Prime Factorization
| 2 | 997, 240, 400, 312 |
| 2 | 997, 120, 200, 156 |
| 2 | 997, 60, 100, 78 |
| 2 | 997, 30, 50, 39 |
| 3 | 997, 15, 25, 39 |
| 5 | 997, 5, 25, 13 |
| 997, 1, 5, 13 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 2 x 3 x 5 x 997 x 1 x 5 x 13 = 15553200
Therefore, the lowest common multiple of 997,240,400,312 is 15553200.
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.
997 x 240 x 400 x 312 = 29862144000
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.
997 : 1, 997
240 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240
400 : 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
312 : 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 997,240,400,312, is 1.
Now, the common factors can be found like this.
997:997
240:2x 2x 2x 2x 3x 5
400:2x 2x 2x 2x 5x 5
312:2x 2x 2x 3x 13
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 5 = 1920
Therefore, the value for common factors is 1920.
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 = 29862144000/(1x1920)
LCM = 29862144000/1920
LCM = 15553200
Thus, we can understand that the LCM of 997,240,400,312 is 15553200.
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FAQs on LCM of 997, 240, 400, 312
1. What is the LCM of 997, 240, 400, 312?
Answer: LCM of 997, 240, 400, 312 is 15553200.
2. How to calculate the LCM of 997, 240, 400, 312?
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 997, 240, 400, 312.
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}.