LCM of 278, 150, 200, 415
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 278, 150, 200, 415 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 278, 150, 200, 415. So, keep reading to learn more.
Given numbers are 278,150,200,415
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 278,150,200,415 is 6922200.
Find LCM of 278,150,200,415 with Prime Factorization
| 2 | 278, 150, 200, 415 |
| 5 | 139, 75, 100, 415 |
| 5 | 139, 15, 20, 83 |
| 139, 3, 4, 83 |
Multiply the prime numbers at the bottom and the left side.
2 x 5 x 5 x 139 x 3 x 4 x 83 = 6922200
Therefore, the lowest common multiple of 278,150,200,415 is 6922200.
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.
278 x 150 x 200 x 415 = 3461100000
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.
278 : 1, 2, 139, 278
150 : 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
200 : 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200
415 : 1, 5, 83, 415
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 278,150,200,415, is 1.
Now, the common factors can be found like this.
278:2x 139
150:2x 3x 5x 5
200:2x 2x 2x 5x 5
415:5x 83
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 5x 5x 5 = 500
Therefore, the value for common factors is 500.
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 = 3461100000/(1x500)
LCM = 3461100000/500
LCM = 6922200
Thus, we can understand that the LCM of 278,150,200,415 is 6922200.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 278, 150, 200, 415
1. What is the LCM of 278, 150, 200, 415?
Answer: LCM of 278, 150, 200, 415 is 6922200.
2. How to calculate the LCM of 278, 150, 200, 415?
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 278, 150, 200, 415.
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}.