LCM of 312, 208, 969, 102
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 312, 208, 969, 102 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 312, 208, 969, 102. So, keep reading to learn more.
Given numbers are 312,208,969,102
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 312,208,969,102 is 201552.
Find LCM of 312,208,969,102 with Prime Factorization
| 2 | 312, 208, 969, 102 |
| 2 | 156, 104, 969, 51 |
| 2 | 78, 52, 969, 51 |
| 3 | 39, 26, 969, 51 |
| 13 | 13, 26, 323, 17 |
| 17 | 1, 2, 323, 17 |
| 1, 2, 19, 1 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 13 x 17 x 1 x 2 x 19 x 1 = 201552
Therefore, the lowest common multiple of 312,208,969,102 is 201552.
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.
312 x 208 x 969 x 102 = 6414190848
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.
312 : 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
208 : 1, 2, 4, 8, 13, 16, 26, 52, 104, 208
969 : 1, 3, 17, 19, 51, 57, 323, 969
102 : 1, 2, 3, 6, 17, 34, 51, 102
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 312,208,969,102, is 1.
Now, the common factors can be found like this.
312:2x 2x 2x 3x 13
208:2x 2x 2x 2x 13
969:3x 17x 19
102:2x 3x 17
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 2x 3x 3x 13x 17 = 31824
Therefore, the value for common factors is 31824.
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 = 6414190848/(1x31824)
LCM = 6414190848/31824
LCM = 201552
Thus, we can understand that the LCM of 312,208,969,102 is 201552.
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FAQs on LCM of 312, 208, 969, 102
1. What is the LCM of 312, 208, 969, 102?
Answer: LCM of 312, 208, 969, 102 is 201552.
2. How to calculate the LCM of 312, 208, 969, 102?
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 312, 208, 969, 102.
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}.