LCM of 724, 120, 104, 310
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 724, 120, 104, 310 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 724, 120, 104, 310. So, keep reading to learn more.
Given numbers are 724,120,104,310
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 724,120,104,310 is 8753160.
Find LCM of 724,120,104,310 with Prime Factorization
| 2 | 724, 120, 104, 310 |
| 2 | 362, 60, 52, 155 |
| 2 | 181, 30, 26, 155 |
| 5 | 181, 15, 13, 155 |
| 181, 3, 13, 31 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 5 x 181 x 3 x 13 x 31 = 8753160
Therefore, the lowest common multiple of 724,120,104,310 is 8753160.
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.
724 x 120 x 104 x 310 = 2801011200
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.
724 : 1, 2, 4, 181, 362, 724
120 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
104 : 1, 2, 4, 8, 13, 26, 52, 104
310 : 1, 2, 5, 10, 31, 62, 155, 310
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 724,120,104,310, is 2.
Now, the common factors can be found like this.
724:2x 2x 181
120:2x 2x 2x 3x 5
104:2x 2x 2x 13
310:2x 5x 31
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 5 = 160
Therefore, the value for common factors is 160.
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 = 2801011200/(2x160)
LCM = 2801011200/320
LCM = 8753160
Thus, we can understand that the LCM of 724,120,104,310 is 8753160.
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FAQs on LCM of 724, 120, 104, 310
1. What is the LCM of 724, 120, 104, 310?
Answer: LCM of 724, 120, 104, 310 is 8753160.
2. How to calculate the LCM of 724, 120, 104, 310?
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 724, 120, 104, 310.
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}.