LCM of 312, 675, 701, 585, 735
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 312, 675, 701, 585, 735 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 312, 675, 701, 585, 735. So, keep reading to learn more.
Given numbers are 312,675,701,585,735
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 312,675,701,585,735 is 2411299800.
Find LCM of 312,675,701,585,735 with Prime Factorization
| 3 | 312, 675, 701, 585, 735 |
| 3 | 104, 225, 701, 195, 245 |
| 5 | 104, 75, 701, 65, 245 |
| 13 | 104, 15, 701, 13, 49 |
| 8, 15, 701, 1, 49 |
Multiply the prime numbers at the bottom and the left side.
3 x 3 x 5 x 13 x 8 x 15 x 701 x 1 x 49 = 2411299800
Therefore, the lowest common multiple of 312,675,701,585,735 is 2411299800.
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.
312 x 675 x 701 x 585 x 735 = 63477467235000
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.
312 : 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
675 : 1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225, 675
701 : 1, 701
585 : 1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195, 585
735 : 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 312,675,701,585,735, is 1.
Now, the common factors can be found like this.
312:2x 2x 2x 3x 13
675:3x 3x 3x 5x 5
701:701
585:3x 3x 5x 13
735:3x 5x 7x 7
From this, we can see that the common factors because they appear for more than two numbers. So, just multiply them all together.
3x 3x 3x 3x 5x 5x 13 = 26325
Therefore, the value for common factors is 26325.
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 = 63477467235000/(1x26325)
LCM = 63477467235000/26325
LCM = 2411299800
Thus, we can understand that the LCM of 312,675,701,585,735 is 2411299800.
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FAQs on LCM of 312, 675, 701, 585, 735
1. What is the LCM of 312, 675, 701, 585, 735?
Answer: LCM of 312, 675, 701, 585, 735 is 2411299800.
2. How to calculate the LCM of 312, 675, 701, 585, 735?
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 312, 675, 701, 585, 735.
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}.