LCM of 210, 750, 138
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 210, 750, 138 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 210, 750, 138. So, keep reading to learn more.
Given numbers are 210,750,138
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 210,750,138 is 120750.
Find LCM of 210,750,138 with Prime Factorization
| 2 | 210, 750, 138 |
| 3 | 105, 375, 69 |
| 5 | 35, 125, 23 |
| 7, 25, 23 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 5 x 7 x 25 x 23 = 120750
Therefore, the lowest common multiple of 210,750,138 is 120750.
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.
210 x 750 x 138 = 21735000
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.
210 : 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
750 : 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375, 750
138 : 1, 2, 3, 6, 23, 46, 69, 138
6 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 210,750,138, is 6.
Now, the common factors can be found like this.
210:2x 3x 5x 7
750:2x 3x 5x 5x 5
138:2x 3x 23
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 = 21735000/(6x30)
LCM = 21735000/180
LCM = 120750
Thus, we can understand that the LCM of 210,750,138 is 120750.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 210, 750, 138
1. What is the LCM of 210, 750, 138?
Answer: LCM of 210, 750, 138 is 120750.
2. How to calculate the LCM of 210, 750, 138?
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 210, 750, 138.
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}.