LCM of 678, 150, 120
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 678, 150, 120 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 678, 150, 120. So, keep reading to learn more.
Given numbers are 678,150,120
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 678,150,120 is 67800.
Find LCM of 678,150,120 with Prime Factorization
| 2 | 678, 150, 120 |
| 3 | 339, 75, 60 |
| 5 | 113, 25, 20 |
| 113, 5, 4 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 5 x 113 x 5 x 4 = 67800
Therefore, the lowest common multiple of 678,150,120 is 67800.
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.
678 x 150 x 120 = 12204000
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.
678 : 1, 2, 3, 6, 113, 226, 339, 678
150 : 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
120 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
6 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 678,150,120, is 6.
Now, the common factors can be found like this.
678:2x 3x 113
150:2x 3x 5x 5
120:2x 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 3x 5 = 30
Therefore, the value for common factors is 30.
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 = 12204000/(6x30)
LCM = 12204000/180
LCM = 67800
Thus, we can understand that the LCM of 678,150,120 is 67800.
LCM of two or more Numbers Calculation Examples
Here are some samples of LCM of two or more Numbers calculations.
FAQs on LCM of 678, 150, 120
1. What is the LCM of 678, 150, 120?
Answer: LCM of 678, 150, 120 is 67800.
2. How to calculate the LCM of 678, 150, 120?
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 678, 150, 120.
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}.