LCM of 705, 309, 377, 515, 414
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 705, 309, 377, 515, 414 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 705, 309, 377, 515, 414. So, keep reading to learn more.
Given numbers are 705,309,377,515,414
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 705,309,377,515,414 is 3777867990.
Find LCM of 705,309,377,515,414 with Prime Factorization
| 3 | 705, 309, 377, 515, 414 |
| 5 | 235, 103, 377, 515, 138 |
| 103 | 47, 103, 377, 103, 138 |
| 47, 1, 377, 1, 138 |
Multiply the prime numbers at the bottom and the left side.
3 x 5 x 103 x 47 x 1 x 377 x 1 x 138 = 3777867990
Therefore, the lowest common multiple of 705,309,377,515,414 is 3777867990.
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.
705 x 309 x 377 x 515 x 414 = 17510418133650
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.
705 : 1, 3, 5, 15, 47, 141, 235, 705
309 : 1, 3, 103, 309
377 : 1, 13, 29, 377
515 : 1, 5, 103, 515
414 : 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 705,309,377,515,414, is 1.
Now, the common factors can be found like this.
705:3x 5x 47
309:3x 103
377:13x 29
515:5x 103
414:2x 3x 3x 23
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 5x 103 = 4635
Therefore, the value for common factors is 4635.
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 = 17510418133650/(1x4635)
LCM = 17510418133650/4635
LCM = 3777867990
Thus, we can understand that the LCM of 705,309,377,515,414 is 3777867990.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 705, 309, 377, 515, 414
1. What is the LCM of 705, 309, 377, 515, 414?
Answer: LCM of 705, 309, 377, 515, 414 is 3777867990.
2. How to calculate the LCM of 705, 309, 377, 515, 414?
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 705, 309, 377, 515, 414.
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}.