LCM of 540, 75, 684
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 540, 75, 684 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, 75, 684. So, keep reading to learn more.
Given numbers are 540,75,684
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 540,75,684 is 51300.
Find LCM of 540,75,684 with Prime Factorization
| 2 | 540, 75, 684 |
| 2 | 270, 75, 342 |
| 3 | 135, 75, 171 |
| 3 | 45, 25, 57 |
| 5 | 15, 25, 19 |
| 3, 5, 19 |
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 19 = 51300
Therefore, the lowest common multiple of 540,75,684 is 51300.
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 75 x 684 = 27702000
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
75 : 1, 3, 5, 15, 25, 75
684 : 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 540,75,684, is 3.
Now, the common factors can be found like this.
540:2x 2x 3x 3x 3x 5
75:3x 5x 5
684:2x 2x 3x 3x 19
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 = 27702000/(3x180)
LCM = 27702000/540
LCM = 51300
Thus, we can understand that the LCM of 540,75,684 is 51300.
LCM of two or more Numbers Calculation Examples
Here are some samples of LCM of two or more Numbers calculations.
FAQs on LCM of 540, 75, 684
1. What is the LCM of 540, 75, 684?
Answer: LCM of 540, 75, 684 is 51300.
2. How to calculate the LCM of 540, 75, 684?
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, 75, 684.
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}.