LCM of 729, 120, 462, 336
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 729, 120, 462, 336 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 729, 120, 462, 336. So, keep reading to learn more.
Given numbers are 729,120,462,336
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 729,120,462,336 is 4490640.
Find LCM of 729,120,462,336 with Prime Factorization
| 2 | 729, 120, 462, 336 |
| 2 | 729, 60, 231, 168 |
| 2 | 729, 30, 231, 84 |
| 3 | 729, 15, 231, 42 |
| 7 | 243, 5, 77, 14 |
| 243, 5, 11, 2 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 7 x 243 x 5 x 11 x 2 = 4490640
Therefore, the lowest common multiple of 729,120,462,336 is 4490640.
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.
729 x 120 x 462 x 336 = 13579695360
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.
729 : 1, 3, 9, 27, 81, 243, 729
120 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
462 : 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462
336 : 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, 336
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 729,120,462,336, is 3.
Now, the common factors can be found like this.
729:3x 3x 3x 3x 3x 3
120:2x 2x 2x 3x 5
462:2x 3x 7x 11
336:2x 2x 2x 2x 3x 7
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 7 = 1008
Therefore, the value for common factors is 1008.
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 = 13579695360/(3x1008)
LCM = 13579695360/3024
LCM = 4490640
Thus, we can understand that the LCM of 729,120,462,336 is 4490640.
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FAQs on LCM of 729, 120, 462, 336
1. What is the LCM of 729, 120, 462, 336?
Answer: LCM of 729, 120, 462, 336 is 4490640.
2. How to calculate the LCM of 729, 120, 462, 336?
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 729, 120, 462, 336.
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}.