LCM of 420, 175, 300, 214
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 420, 175, 300, 214 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 420, 175, 300, 214. So, keep reading to learn more.
Given numbers are 420,175,300,214
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 420,175,300,214 is 224700.
Find LCM of 420,175,300,214 with Prime Factorization
| 2 | 420, 175, 300, 214 |
| 2 | 210, 175, 150, 107 |
| 3 | 105, 175, 75, 107 |
| 5 | 35, 175, 25, 107 |
| 5 | 7, 35, 5, 107 |
| 7 | 7, 7, 1, 107 |
| 1, 1, 1, 107 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 5 x 5 x 7 x 1 x 1 x 1 x 107 = 224700
Therefore, the lowest common multiple of 420,175,300,214 is 224700.
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.
420 x 175 x 300 x 214 = 4718700000
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.
420 : 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
175 : 1, 5, 7, 25, 35, 175
300 : 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300
214 : 1, 2, 107, 214
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 420,175,300,214, is 1.
Now, the common factors can be found like this.
420:2x 2x 3x 5x 7
175:5x 5x 7
300:2x 2x 3x 5x 5
214:2x 107
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 3x 5x 5x 5x 7 = 21000
Therefore, the value for common factors is 21000.
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 = 4718700000/(1x21000)
LCM = 4718700000/21000
LCM = 224700
Thus, we can understand that the LCM of 420,175,300,214 is 224700.
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FAQs on LCM of 420, 175, 300, 214
1. What is the LCM of 420, 175, 300, 214?
Answer: LCM of 420, 175, 300, 214 is 224700.
2. How to calculate the LCM of 420, 175, 300, 214?
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 420, 175, 300, 214.
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}.