LCM of 645, 240, 189, 678
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 645, 240, 189, 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 645, 240, 189, 678. So, keep reading to learn more.
Given numbers are 645,240,189,678
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 645,240,189,678 is 73468080.
Find LCM of 645,240,189,678 with Prime Factorization
| 2 | 645, 240, 189, 678 |
| 3 | 645, 120, 189, 339 |
| 5 | 215, 40, 63, 113 |
| 43, 8, 63, 113 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 5 x 43 x 8 x 63 x 113 = 73468080
Therefore, the lowest common multiple of 645,240,189,678 is 73468080.
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.
645 x 240 x 189 x 678 = 19836381600
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.
645 : 1, 3, 5, 15, 43, 129, 215, 645
240 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240
189 : 1, 3, 7, 9, 21, 27, 63, 189
678 : 1, 2, 3, 6, 113, 226, 339, 678
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 645,240,189,678, is 3.
Now, the common factors can be found like this.
645:3x 5x 43
240:2x 2x 2x 2x 3x 5
189:3x 3x 3x 7
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 3x 3x 5 = 90
Therefore, the value for common factors is 90.
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 = 19836381600/(3x90)
LCM = 19836381600/270
LCM = 73468080
Thus, we can understand that the LCM of 645,240,189,678 is 73468080.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 645, 240, 189, 678
1. What is the LCM of 645, 240, 189, 678?
Answer: LCM of 645, 240, 189, 678 is 73468080.
2. How to calculate the LCM of 645, 240, 189, 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 645, 240, 189, 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}.