LCM of 456, 540, 960
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 456, 540, 960 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 456, 540, 960. So, keep reading to learn more.
Given numbers are 456,540,960
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 456,540,960 is 164160.
Find LCM of 456,540,960 with Prime Factorization
| 2 | 456, 540, 960 |
| 2 | 228, 270, 480 |
| 2 | 114, 135, 240 |
| 3 | 57, 135, 120 |
| 5 | 19, 45, 40 |
| 19, 9, 8 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 5 x 19 x 9 x 8 = 164160
Therefore, the lowest common multiple of 456,540,960 is 164160.
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.
456 x 540 x 960 = 236390400
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.
456 : 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456
540 : 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540
960 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960
12 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 456,540,960, is 12.
Now, the common factors can be found like this.
456:2x 2x 2x 3x 19
540:2x 2x 3x 3x 3x 5
960:2x 2x 2x 2x 2x 2x 3x 5
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 5 = 120
Therefore, the value for common factors is 120.
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 = 236390400/(12x120)
LCM = 236390400/1440
LCM = 164160
Thus, we can understand that the LCM of 456,540,960 is 164160.
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FAQs on LCM of 456, 540, 960
1. What is the LCM of 456, 540, 960?
Answer: LCM of 456, 540, 960 is 164160.
2. How to calculate the LCM of 456, 540, 960?
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 456, 540, 960.
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}.