LCM of 800, 240, 748, 419
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 800, 240, 748, 419 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 800, 240, 748, 419. So, keep reading to learn more.
Given numbers are 800,240,748,419
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 800,240,748,419 is 188047200.
Find LCM of 800,240,748,419 with Prime Factorization
| 2 | 800, 240, 748, 419 |
| 2 | 400, 120, 374, 419 |
| 2 | 200, 60, 187, 419 |
| 2 | 100, 30, 187, 419 |
| 5 | 50, 15, 187, 419 |
| 10, 3, 187, 419 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 2 x 5 x 10 x 3 x 187 x 419 = 188047200
Therefore, the lowest common multiple of 800,240,748,419 is 188047200.
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.
800 x 240 x 748 x 419 = 60175104000
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.
800 : 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400, 800
240 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240
748 : 1, 2, 4, 11, 17, 22, 34, 44, 68, 187, 374, 748
419 : 1, 419
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 800,240,748,419, is 1.
Now, the common factors can be found like this.
800:2x 2x 2x 2x 2x 5x 5
240:2x 2x 2x 2x 3x 5
748:2x 2x 11x 17
419:419
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 5 = 320
Therefore, the value for common factors is 320.
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 = 60175104000/(1x320)
LCM = 60175104000/320
LCM = 188047200
Thus, we can understand that the LCM of 800,240,748,419 is 188047200.
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FAQs on LCM of 800, 240, 748, 419
1. What is the LCM of 800, 240, 748, 419?
Answer: LCM of 800, 240, 748, 419 is 188047200.
2. How to calculate the LCM of 800, 240, 748, 419?
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 800, 240, 748, 419.
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}.