LCM of 105, 132, 314, 361
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 105, 132, 314, 361 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, 132, 314, 361. So, keep reading to learn more.
Given numbers are 105,132,314,361
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 105,132,314,361 is 261847740.
Find LCM of 105,132,314,361 with Prime Factorization
| 2 | 105, 132, 314, 361 |
| 3 | 105, 66, 157, 361 |
| 35, 22, 157, 361 |
Multiply the prime numbers at the bottom and the left side.
2 x 3 x 35 x 22 x 157 x 361 = 261847740
Therefore, the lowest common multiple of 105,132,314,361 is 261847740.
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 132 x 314 x 361 = 1571086440
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
132 : 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132
314 : 1, 2, 157, 314
361 : 1, 19, 361
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 105,132,314,361, is 1.
Now, the common factors can be found like this.
105:3x 5x 7
132:2x 2x 3x 11
314:2x 157
361:19x 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 3 = 6
Therefore, the value for common factors is 6.
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 = 1571086440/(1x6)
LCM = 1571086440/6
LCM = 261847740
Thus, we can understand that the LCM of 105,132,314,361 is 261847740.
LCM of two or more Numbers Calculation Examples
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FAQs on LCM of 105, 132, 314, 361
1. What is the LCM of 105, 132, 314, 361?
Answer: LCM of 105, 132, 314, 361 is 261847740.
2. How to calculate the LCM of 105, 132, 314, 361?
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, 132, 314, 361.
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}.