LCM of 689, 120, 412, 198
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 689, 120, 412, 198 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 689, 120, 412, 198. So, keep reading to learn more.
Given numbers are 689,120,412,198
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 689,120,412,198 is 281029320.
Find LCM of 689,120,412,198 with Prime Factorization
| 2 | 689, 120, 412, 198 |
| 2 | 689, 60, 206, 99 |
| 3 | 689, 30, 103, 99 |
| 689, 10, 103, 33 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 689 x 10 x 103 x 33 = 281029320
Therefore, the lowest common multiple of 689,120,412,198 is 281029320.
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.
689 x 120 x 412 x 198 = 6744703680
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.
689 : 1, 13, 53, 689
120 : 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
412 : 1, 2, 4, 103, 206, 412
198 : 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 689,120,412,198, is 1.
Now, the common factors can be found like this.
689:13x 53
120:2x 2x 2x 3x 5
412:2x 2x 103
198:2x 3x 3x 11
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 3 = 24
Therefore, the value for common factors is 24.
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 = 6744703680/(1x24)
LCM = 6744703680/24
LCM = 281029320
Thus, we can understand that the LCM of 689,120,412,198 is 281029320.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 689, 120, 412, 198
1. What is the LCM of 689, 120, 412, 198?
Answer: LCM of 689, 120, 412, 198 is 281029320.
2. How to calculate the LCM of 689, 120, 412, 198?
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 689, 120, 412, 198.
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}.