LCM of 540, 900, 678
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 540, 900, 678 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 540, 900, 678. So, keep reading to learn more.
Given numbers are 540,900,678
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 540,900,678 is 305100.
Find LCM of 540,900,678 with Prime Factorization
| 2 | 540, 900, 678 |
| 2 | 270, 450, 339 |
| 3 | 135, 225, 339 |
| 3 | 45, 75, 113 |
| 5 | 15, 25, 113 |
| 3, 5, 113 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 3 x 5 x 3 x 5 x 113 = 305100
Therefore, the lowest common multiple of 540,900,678 is 305100.
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.
540 x 900 x 678 = 329508000
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.
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
900 : 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 900
678 : 1, 2, 3, 6, 113, 226, 339, 678
6 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 540,900,678, is 6.
Now, the common factors can be found like this.
540:2x 2x 3x 3x 3x 5
900:2x 2x 3x 3x 5x 5
678:2x 3x 113
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 3x 5 = 180
Therefore, the value for common factors is 180.
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 = 329508000/(6x180)
LCM = 329508000/1080
LCM = 305100
Thus, we can understand that the LCM of 540,900,678 is 305100.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 540, 900, 678
1. What is the LCM of 540, 900, 678?
Answer: LCM of 540, 900, 678 is 305100.
2. How to calculate the LCM of 540, 900, 678?
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 540, 900, 678.
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}.