LCM of 735, 135, 708, 678, 687
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 735, 135, 708, 678, 687 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 735, 135, 708, 678, 687. So, keep reading to learn more.
Given numbers are 735,135,708,678,687
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 735,135,708,678,687 is 40397619780.
Find LCM of 735,135,708,678,687 with Prime Factorization
| 2 | 735, 135, 708, 678, 687 |
| 3 | 735, 135, 354, 339, 687 |
| 5 | 245, 45, 118, 113, 229 |
| 49, 9, 118, 113, 229 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 5 x 49 x 9 x 118 x 113 x 229 = 40397619780
Therefore, the lowest common multiple of 735,135,708,678,687 is 40397619780.
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.
735 x 135 x 708 x 678 x 687 = 32722072021800
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.
735 : 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735
135 : 1, 3, 5, 9, 15, 27, 45, 135
708 : 1, 2, 3, 4, 6, 12, 59, 118, 177, 236, 354, 708
678 : 1, 2, 3, 6, 113, 226, 339, 678
687 : 1, 3, 229, 687
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 735,135,708,678,687, is 3.
Now, the common factors can be found like this.
735:3x 5x 7x 7
135:3x 3x 3x 5
708:2x 2x 3x 59
678:2x 3x 113
687:3x 229
From this, we can see that the common factors because they appear for more than two numbers. So, just multiply them all together.
2x 3x 3x 3x 5 = 270
Therefore, the value for common factors is 270.
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 = 32722072021800/(3x270)
LCM = 32722072021800/810
LCM = 40397619780
Thus, we can understand that the LCM of 735,135,708,678,687 is 40397619780.
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FAQs on LCM of 735, 135, 708, 678, 687
1. What is the LCM of 735, 135, 708, 678, 687?
Answer: LCM of 735, 135, 708, 678, 687 is 40397619780.
2. How to calculate the LCM of 735, 135, 708, 678, 687?
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 735, 135, 708, 678, 687.
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}.