LCM of 120, 420, 138, 560
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 120, 420, 138, 560 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 120, 420, 138, 560. So, keep reading to learn more.
Given numbers are 120,420,138,560
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 120,420,138,560 is 38640.
Find LCM of 120,420,138,560 with Prime Factorization
| 2 | 120, 420, 138, 560 |
| 2 | 60, 210, 69, 280 |
| 2 | 30, 105, 69, 140 |
| 3 | 15, 105, 69, 70 |
| 5 | 5, 35, 23, 70 |
| 7 | 1, 7, 23, 14 |
| 1, 1, 23, 2 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 5 x 7 x 1 x 1 x 23 x 2 = 38640
Therefore, the lowest common multiple of 120,420,138,560 is 38640.
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.
120 x 420 x 138 x 560 = 3894912000
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.
120 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
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
138 : 1, 2, 3, 6, 23, 46, 69, 138
560 : 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, 560
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 120,420,138,560, is 2.
Now, the common factors can be found like this.
120:2x 2x 2x 3x 5
420:2x 2x 3x 5x 7
138:2x 3x 23
560:2x 2x 2x 2x 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 2x 2x 3x 3x 5x 5x 7 = 50400
Therefore, the value for common factors is 50400.
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 = 3894912000/(2x50400)
LCM = 3894912000/100800
LCM = 38640
Thus, we can understand that the LCM of 120,420,138,560 is 38640.
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FAQs on LCM of 120, 420, 138, 560
1. What is the LCM of 120, 420, 138, 560?
Answer: LCM of 120, 420, 138, 560 is 38640.
2. How to calculate the LCM of 120, 420, 138, 560?
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 120, 420, 138, 560.
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}.