LCM of 735, 105, 320, 415, 714
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 735, 105, 320, 415, 714 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, 105, 320, 415, 714. So, keep reading to learn more.
Given numbers are 735,105,320,415,714
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 735,105,320,415,714 is 66373440.
Find LCM of 735,105,320,415,714 with Prime Factorization
| 2 | 735, 105, 320, 415, 714 |
| 3 | 735, 105, 160, 415, 357 |
| 5 | 245, 35, 160, 415, 119 |
| 7 | 49, 7, 32, 83, 119 |
| 1, 7, 32, 83, 17 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 5 x 7 x 1 x 7 x 32 x 83 x 17 = 66373440
Therefore, the lowest common multiple of 735,105,320,415,714 is 66373440.
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 105 x 320 x 415 x 714 = 7317671760000
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
105 : 1, 3, 5, 7, 15, 21, 35, 105
320 : 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 320
415 : 1, 5, 83, 415
714 : 1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357, 714
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 735,105,320,415,714, is 1.
Now, the common factors can be found like this.
735:3x 5x 7x 7
105:3x 5x 7
320:2x 2x 2x 2x 2x 2x 5
415:5x 83
714:2x 3x 7x 17
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 5x 5x 5x 7x 7 = 110250
Therefore, the value for common factors is 110250.
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 = 7317671760000/(1x110250)
LCM = 7317671760000/110250
LCM = 66373440
Thus, we can understand that the LCM of 735,105,320,415,714 is 66373440.
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FAQs on LCM of 735, 105, 320, 415, 714
1. What is the LCM of 735, 105, 320, 415, 714?
Answer: LCM of 735, 105, 320, 415, 714 is 66373440.
2. How to calculate the LCM of 735, 105, 320, 415, 714?
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, 105, 320, 415, 714.
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}.