LCM of 174, 126, 315
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 174, 126, 315 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 174, 126, 315. So, keep reading to learn more.
Given numbers are 174,126,315
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 174,126,315 is 18270.
Find LCM of 174,126,315 with Prime Factorization
| 2 | 174, 126, 315 |
| 3 | 87, 63, 315 |
| 3 | 29, 21, 105 |
| 7 | 29, 7, 35 |
| 29, 1, 5 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 3 x 7 x 29 x 1 x 5 = 18270
Therefore, the lowest common multiple of 174,126,315 is 18270.
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.
174 x 126 x 315 = 6906060
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.
174 : 1, 2, 3, 6, 29, 58, 87, 174
126 : 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126
315 : 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 174,126,315, is 3.
Now, the common factors can be found like this.
174:2x 3x 29
126:2x 3x 3x 7
315:3x 3x 5x 7
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 7 = 126
Therefore, the value for common factors is 126.
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 = 6906060/(3x126)
LCM = 6906060/378
LCM = 18270
Thus, we can understand that the LCM of 174,126,315 is 18270.
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FAQs on LCM of 174, 126, 315
1. What is the LCM of 174, 126, 315?
Answer: LCM of 174, 126, 315 is 18270.
2. How to calculate the LCM of 174, 126, 315?
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 174, 126, 315.
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}.