LCM of 705, 310, 414, 420, 768
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 705, 310, 414, 420, 768 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, 310, 414, 420, 768. So, keep reading to learn more.
Given numbers are 705,310,414,420,768
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 705,310,414,420,768 is 2702327040.
Find LCM of 705,310,414,420,768 with Prime Factorization
| 2 | 705, 310, 414, 420, 768 |
| 2 | 705, 155, 207, 210, 384 |
| 3 | 705, 155, 207, 105, 192 |
| 5 | 235, 155, 69, 35, 64 |
| 47, 31, 69, 7, 64 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 5 x 47 x 31 x 69 x 7 x 64 = 2702327040
Therefore, the lowest common multiple of 705,310,414,420,768 is 2702327040.
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 310 x 414 x 420 x 768 = 29185132032000
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
310 : 1, 2, 5, 10, 31, 62, 155, 310
414 : 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
420 : 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
768 : 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 705,310,414,420,768, is 1.
Now, the common factors can be found like this.
705:3x 5x 47
310:2x 5x 31
414:2x 3x 3x 23
420:2x 2x 3x 5x 7
768:2x 2x 2x 2x 2x 2x 2x 2x 3
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 3x 3x 3x 5x 5 = 10800
Therefore, the value for common factors is 10800.
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 = 29185132032000/(1x10800)
LCM = 29185132032000/10800
LCM = 2702327040
Thus, we can understand that the LCM of 705,310,414,420,768 is 2702327040.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 705, 310, 414, 420, 768
1. What is the LCM of 705, 310, 414, 420, 768?
Answer: LCM of 705, 310, 414, 420, 768 is 2702327040.
2. How to calculate the LCM of 705, 310, 414, 420, 768?
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, 310, 414, 420, 768.
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}.