LCM of 105, 420, 138, 209
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 105, 420, 138, 209 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 105, 420, 138, 209. So, keep reading to learn more.
Given numbers are 105,420,138,209
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 105,420,138,209 is 2018940.
Find LCM of 105,420,138,209 with Prime Factorization
| 2 | 105, 420, 138, 209 |
| 3 | 105, 210, 69, 209 |
| 5 | 35, 70, 23, 209 |
| 7 | 7, 14, 23, 209 |
| 1, 2, 23, 209 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 5 x 7 x 1 x 2 x 23 x 209 = 2018940
Therefore, the lowest common multiple of 105,420,138,209 is 2018940.
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.
105 x 420 x 138 x 209 = 1271932200
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.
105 : 1, 3, 5, 7, 15, 21, 35, 105
420 : 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
138 : 1, 2, 3, 6, 23, 46, 69, 138
209 : 1, 11, 19, 209
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 105,420,138,209, is 1.
Now, the common factors can be found like this.
105:3x 5x 7
420:2x 2x 3x 5x 7
138:2x 3x 23
209:11x 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 3x 3x 5x 7 = 630
Therefore, the value for common factors is 630.
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 = 1271932200/(1x630)
LCM = 1271932200/630
LCM = 2018940
Thus, we can understand that the LCM of 105,420,138,209 is 2018940.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 105, 420, 138, 209
1. What is the LCM of 105, 420, 138, 209?
Answer: LCM of 105, 420, 138, 209 is 2018940.
2. How to calculate the LCM of 105, 420, 138, 209?
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 105, 420, 138, 209.
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}.