LCM of 728, 320, 456, 724
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 728, 320, 456, 724 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 728, 320, 456, 724. So, keep reading to learn more.
Given numbers are 728,320,456,724
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 728,320,456,724 is 300431040.
Find LCM of 728,320,456,724 with Prime Factorization
| 2 | 728, 320, 456, 724 |
| 2 | 364, 160, 228, 362 |
| 2 | 182, 80, 114, 181 |
| 91, 40, 57, 181 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 91 x 40 x 57 x 181 = 300431040
Therefore, the lowest common multiple of 728,320,456,724 is 300431040.
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.
728 x 320 x 456 x 724 = 76910346240
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.
728 : 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728
320 : 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 320
456 : 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456
724 : 1, 2, 4, 181, 362, 724
4 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 728,320,456,724, is 4.
Now, the common factors can be found like this.
728:2x 2x 2x 7x 13
320:2x 2x 2x 2x 2x 2x 5
456:2x 2x 2x 3x 19
724:2x 2x 181
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 2x 2 = 64
Therefore, the value for common factors is 64.
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 = 76910346240/(4x64)
LCM = 76910346240/256
LCM = 300431040
Thus, we can understand that the LCM of 728,320,456,724 is 300431040.
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FAQs on LCM of 728, 320, 456, 724
1. What is the LCM of 728, 320, 456, 724?
Answer: LCM of 728, 320, 456, 724 is 300431040.
2. How to calculate the LCM of 728, 320, 456, 724?
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 728, 320, 456, 724.
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}.