LCM of 135, 840, 674, 684, 900
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 135, 840, 674, 684, 900 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 135, 840, 674, 684, 900. So, keep reading to learn more.
Given numbers are 135,840,674,684,900
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 135,840,674,684,900 is 242033400.
Find LCM of 135,840,674,684,900 with Prime Factorization
| 2 | 135, 840, 674, 684, 900 |
| 2 | 135, 420, 337, 342, 450 |
| 3 | 135, 210, 337, 171, 225 |
| 3 | 45, 70, 337, 57, 75 |
| 5 | 15, 70, 337, 19, 25 |
| 3, 14, 337, 19, 5 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 3 x 5 x 3 x 14 x 337 x 19 x 5 = 242033400
Therefore, the lowest common multiple of 135,840,674,684,900 is 242033400.
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.
135 x 840 x 674 x 684 x 900 = 47051292960000
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.
135 : 1, 3, 5, 9, 15, 27, 45, 135
840 : 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840
674 : 1, 2, 337, 674
684 : 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684
900 : 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 900
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 135,840,674,684,900, is 1.
Now, the common factors can be found like this.
135:3x 3x 3x 5
840:2x 2x 2x 3x 5x 7
674:2x 337
684:2x 2x 3x 3x 19
900:2x 2x 3x 3x 5x 5
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 3x 3x 3x 3x 3x 5x 5 = 194400
Therefore, the value for common factors is 194400.
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 = 47051292960000/(1x194400)
LCM = 47051292960000/194400
LCM = 242033400
Thus, we can understand that the LCM of 135,840,674,684,900 is 242033400.
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FAQs on LCM of 135, 840, 674, 684, 900
1. What is the LCM of 135, 840, 674, 684, 900?
Answer: LCM of 135, 840, 674, 684, 900 is 242033400.
2. How to calculate the LCM of 135, 840, 674, 684, 900?
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 135, 840, 674, 684, 900.
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}.