LCM of 312, 496, 611, 170, 105
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 312, 496, 611, 170, 105 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, 496, 611, 170, 105. So, keep reading to learn more.
Given numbers are 312,496,611,170,105
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 312,496,611,170,105 is 540954960.
Find LCM of 312,496,611,170,105 with Prime Factorization
| 2 | 312, 496, 611, 170, 105 |
| 2 | 156, 248, 611, 85, 105 |
| 2 | 78, 124, 611, 85, 105 |
| 3 | 39, 62, 611, 85, 105 |
| 5 | 13, 62, 611, 85, 35 |
| 13 | 13, 62, 611, 17, 7 |
| 1, 62, 47, 17, 7 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 5 x 13 x 1 x 62 x 47 x 17 x 7 = 540954960
Therefore, the lowest common multiple of 312,496,611,170,105 is 540954960.
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 496 x 611 x 170 x 105 = 1687779475200
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
496 : 1, 2, 4, 8, 16, 31, 62, 124, 248, 496
611 : 1, 13, 47, 611
170 : 1, 2, 5, 10, 17, 34, 85, 170
105 : 1, 3, 5, 7, 15, 21, 35, 105
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 312,496,611,170,105, is 1.
Now, the common factors can be found like this.
312:2x 2x 2x 3x 13
496:2x 2x 2x 2x 31
611:13x 47
170:2x 5x 17
105:3x 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 2x 2x 2x 3x 5x 13 = 3120
Therefore, the value for common factors is 3120.
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 = 1687779475200/(1x3120)
LCM = 1687779475200/3120
LCM = 540954960
Thus, we can understand that the LCM of 312,496,611,170,105 is 540954960.
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FAQs on LCM of 312, 496, 611, 170, 105
1. What is the LCM of 312, 496, 611, 170, 105?
Answer: LCM of 312, 496, 611, 170, 105 is 540954960.
2. How to calculate the LCM of 312, 496, 611, 170, 105?
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, 496, 611, 170, 105.
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}.