LCM of 114, 742, 414, 200, 306
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 114, 742, 414, 200, 306 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 114, 742, 414, 200, 306. So, keep reading to learn more.
Given numbers are 114,742,414,200,306
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 114,742,414,200,306 is 4961086200.
Find LCM of 114,742,414,200,306 with Prime Factorization
| 2 | 114, 742, 414, 200, 306 |
| 3 | 57, 371, 207, 100, 153 |
| 3 | 19, 371, 69, 100, 51 |
| 19, 371, 23, 100, 17 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 3 x 19 x 371 x 23 x 100 x 17 = 4961086200
Therefore, the lowest common multiple of 114,742,414,200,306 is 4961086200.
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.
114 x 742 x 414 x 200 x 306 = 2143189238400
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.
114 : 1, 2, 3, 6, 19, 38, 57, 114
742 : 1, 2, 7, 14, 53, 106, 371, 742
414 : 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
200 : 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200
306 : 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 114,742,414,200,306, is 2.
Now, the common factors can be found like this.
114:2x 3x 19
742:2x 7x 53
414:2x 3x 3x 23
200:2x 2x 2x 5x 5
306:2x 3x 3x 17
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 3x 3 = 216
Therefore, the value for common factors is 216.
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 = 2143189238400/(2x216)
LCM = 2143189238400/432
LCM = 4961086200
Thus, we can understand that the LCM of 114,742,414,200,306 is 4961086200.
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FAQs on LCM of 114, 742, 414, 200, 306
1. What is the LCM of 114, 742, 414, 200, 306?
Answer: LCM of 114, 742, 414, 200, 306 is 4961086200.
2. How to calculate the LCM of 114, 742, 414, 200, 306?
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 114, 742, 414, 200, 306.
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}.