LCM of 748, 724, 105, 493
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 748, 724, 105, 493 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 748, 724, 105, 493. So, keep reading to learn more.
Given numbers are 748,724,105,493
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 748,724,105,493 is 412256460.
Find LCM of 748,724,105,493 with Prime Factorization
| 2 | 748, 724, 105, 493 |
| 2 | 374, 362, 105, 493 |
| 17 | 187, 181, 105, 493 |
| 11, 181, 105, 29 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 17 x 11 x 181 x 105 x 29 = 412256460
Therefore, the lowest common multiple of 748,724,105,493 is 412256460.
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.
748 x 724 x 105 x 493 = 28033439280
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.
748 : 1, 2, 4, 11, 17, 22, 34, 44, 68, 187, 374, 748
724 : 1, 2, 4, 181, 362, 724
105 : 1, 3, 5, 7, 15, 21, 35, 105
493 : 1, 17, 29, 493
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 748,724,105,493, is 1.
Now, the common factors can be found like this.
748:2x 2x 11x 17
724:2x 2x 181
105:3x 5x 7
493:17x 29
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 17 = 68
Therefore, the value for common factors is 68.
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 = 28033439280/(1x68)
LCM = 28033439280/68
LCM = 412256460
Thus, we can understand that the LCM of 748,724,105,493 is 412256460.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 748, 724, 105, 493
1. What is the LCM of 748, 724, 105, 493?
Answer: LCM of 748, 724, 105, 493 is 412256460.
2. How to calculate the LCM of 748, 724, 105, 493?
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 748, 724, 105, 493.
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}.