LCM of 726, 120, 234, 420
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 726, 120, 234, 420 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 726, 120, 234, 420. So, keep reading to learn more.
Given numbers are 726,120,234,420
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 726,120,234,420 is 3963960.
Find LCM of 726,120,234,420 with Prime Factorization
| 2 | 726, 120, 234, 420 |
| 2 | 363, 60, 117, 210 |
| 3 | 363, 30, 117, 105 |
| 5 | 121, 10, 39, 35 |
| 121, 2, 39, 7 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 5 x 121 x 2 x 39 x 7 = 3963960
Therefore, the lowest common multiple of 726,120,234,420 is 3963960.
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.
726 x 120 x 234 x 420 = 8562153600
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.
726 : 1, 2, 3, 6, 11, 22, 33, 66, 121, 242, 363, 726
120 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
234 : 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234
420 : 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
6 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 726,120,234,420, is 6.
Now, the common factors can be found like this.
726:2x 3x 11x 11
120:2x 2x 2x 3x 5
234:2x 3x 3x 13
420:2x 2x 3x 5x 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 3x 3x 5 = 360
Therefore, the value for common factors is 360.
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 = 8562153600/(6x360)
LCM = 8562153600/2160
LCM = 3963960
Thus, we can understand that the LCM of 726,120,234,420 is 3963960.
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FAQs on LCM of 726, 120, 234, 420
1. What is the LCM of 726, 120, 234, 420?
Answer: LCM of 726, 120, 234, 420 is 3963960.
2. How to calculate the LCM of 726, 120, 234, 420?
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 726, 120, 234, 420.
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}.