LCM of 735, 240, 825, 416
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 735, 240, 825, 416 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, 240, 825, 416. So, keep reading to learn more.
Given numbers are 735,240,825,416
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 735,240,825,416 is 16816800.
Find LCM of 735,240,825,416 with Prime Factorization
| 2 | 735, 240, 825, 416 |
| 2 | 735, 120, 825, 208 |
| 2 | 735, 60, 825, 104 |
| 2 | 735, 30, 825, 52 |
| 3 | 735, 15, 825, 26 |
| 5 | 245, 5, 275, 26 |
| 49, 1, 55, 26 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 2 x 3 x 5 x 49 x 1 x 55 x 26 = 16816800
Therefore, the lowest common multiple of 735,240,825,416 is 16816800.
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 240 x 825 x 416 = 60540480000
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
240 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240
825 : 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825
416 : 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 735,240,825,416, is 1.
Now, the common factors can be found like this.
735:3x 5x 7x 7
240:2x 2x 2x 2x 3x 5
825:3x 5x 5x 11
416:2x 2x 2x 2x 2x 13
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 5x 5 = 3600
Therefore, the value for common factors is 3600.
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 = 60540480000/(1x3600)
LCM = 60540480000/3600
LCM = 16816800
Thus, we can understand that the LCM of 735,240,825,416 is 16816800.
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FAQs on LCM of 735, 240, 825, 416
1. What is the LCM of 735, 240, 825, 416?
Answer: LCM of 735, 240, 825, 416 is 16816800.
2. How to calculate the LCM of 735, 240, 825, 416?
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, 240, 825, 416.
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}.