LCM of 471, 540, 500, 208, 975
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 471, 540, 500, 208, 975 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 471, 540, 500, 208, 975. So, keep reading to learn more.
Given numbers are 471,540,500,208,975
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 471,540,500,208,975 is 110214000.
Find LCM of 471,540,500,208,975 with Prime Factorization
| 2 | 471, 540, 500, 208, 975 |
| 2 | 471, 270, 250, 104, 975 |
| 3 | 471, 135, 125, 52, 975 |
| 5 | 157, 45, 125, 52, 325 |
| 5 | 157, 9, 25, 52, 65 |
| 13 | 157, 9, 5, 52, 13 |
| 157, 9, 5, 4, 1 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 5 x 5 x 13 x 157 x 9 x 5 x 4 x 1 = 110214000
Therefore, the lowest common multiple of 471,540,500,208,975 is 110214000.
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.
471 x 540 x 500 x 208 x 975 = 25790076000000
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.
471 : 1, 3, 157, 471
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
500 : 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500
208 : 1, 2, 4, 8, 13, 16, 26, 52, 104, 208
975 : 1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, 975
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 471,540,500,208,975, is 1.
Now, the common factors can be found like this.
471:3x 157
540:2x 2x 3x 3x 3x 5
500:2x 2x 5x 5x 5
208:2x 2x 2x 2x 13
975:3x 5x 5x 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 3x 3x 5x 5x 5x 13 = 234000
Therefore, the value for common factors is 234000.
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 = 25790076000000/(1x234000)
LCM = 25790076000000/234000
LCM = 110214000
Thus, we can understand that the LCM of 471,540,500,208,975 is 110214000.
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FAQs on LCM of 471, 540, 500, 208, 975
1. What is the LCM of 471, 540, 500, 208, 975?
Answer: LCM of 471, 540, 500, 208, 975 is 110214000.
2. How to calculate the LCM of 471, 540, 500, 208, 975?
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 471, 540, 500, 208, 975.
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}.