LCM of 724, 338, 345, 414
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 724, 338, 345, 414 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, 338, 345, 414. So, keep reading to learn more.
Given numbers are 724,338,345,414
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 724,338,345,414 is 126638460.
Find LCM of 724,338,345,414 with Prime Factorization
| 2 | 724, 338, 345, 414 |
| 3 | 362, 169, 345, 207 |
| 23 | 362, 169, 115, 69 |
| 362, 169, 5, 3 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 23 x 362 x 169 x 5 x 3 = 126638460
Therefore, the lowest common multiple of 724,338,345,414 is 126638460.
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 338 x 345 x 414 = 34952214960
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
338 : 1, 2, 13, 26, 169, 338
345 : 1, 3, 5, 15, 23, 69, 115, 345
414 : 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 724,338,345,414, is 1.
Now, the common factors can be found like this.
724:2x 2x 181
338:2x 13x 13
345:3x 5x 23
414:2x 3x 3x 23
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 3x 23 = 276
Therefore, the value for common factors is 276.
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 = 34952214960/(1x276)
LCM = 34952214960/276
LCM = 126638460
Thus, we can understand that the LCM of 724,338,345,414 is 126638460.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 724, 338, 345, 414
1. What is the LCM of 724, 338, 345, 414?
Answer: LCM of 724, 338, 345, 414 is 126638460.
2. How to calculate the LCM of 724, 338, 345, 414?
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, 338, 345, 414.
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}.