LCM of 705, 517, 478, 972, 240
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 705, 517, 478, 972, 240 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, 517, 478, 972, 240. So, keep reading to learn more.
Given numbers are 705,517,478,972,240
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 705,517,478,972,240 is 2402064720.
Find LCM of 705,517,478,972,240 with Prime Factorization
| 2 | 705, 517, 478, 972, 240 |
| 2 | 705, 517, 239, 486, 120 |
| 3 | 705, 517, 239, 243, 60 |
| 5 | 235, 517, 239, 81, 20 |
| 47 | 47, 517, 239, 81, 4 |
| 1, 11, 239, 81, 4 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 5 x 47 x 1 x 11 x 239 x 81 x 4 = 2402064720
Therefore, the lowest common multiple of 705,517,478,972,240 is 2402064720.
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 517 x 478 x 972 x 240 = 40642935062400
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
517 : 1, 11, 47, 517
478 : 1, 2, 239, 478
972 : 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972
240 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 705,517,478,972,240, is 1.
Now, the common factors can be found like this.
705:3x 5x 47
517:11x 47
478:2x 239
972:2x 2x 3x 3x 3x 3x 3
240:2x 2x 2x 2x 3x 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 3x 3x 5x 47 = 16920
Therefore, the value for common factors is 16920.
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 = 40642935062400/(1x16920)
LCM = 40642935062400/16920
LCM = 2402064720
Thus, we can understand that the LCM of 705,517,478,972,240 is 2402064720.
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FAQs on LCM of 705, 517, 478, 972, 240
1. What is the LCM of 705, 517, 478, 972, 240?
Answer: LCM of 705, 517, 478, 972, 240 is 2402064720.
2. How to calculate the LCM of 705, 517, 478, 972, 240?
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, 517, 478, 972, 240.
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}.