LCM of 90, 53, 16, 78, 312
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 90, 53, 16, 78, 312 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 90, 53, 16, 78, 312. So, keep reading to learn more.
Given numbers are 90,53,16,78,312
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 90,53,16,78,312 is 496080.
Find LCM of 90,53,16,78,312 with Prime Factorization
| 2 | 90, 53, 16, 78, 312 |
| 2 | 45, 53, 8, 39, 156 |
| 2 | 45, 53, 4, 39, 78 |
| 3 | 45, 53, 2, 39, 39 |
| 13 | 15, 53, 2, 13, 13 |
| 15, 53, 2, 1, 1 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 3 x 13 x 15 x 53 x 2 x 1 x 1 = 496080
Therefore, the lowest common multiple of 90,53,16,78,312 is 496080.
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.
90 x 53 x 16 x 78 x 312 = 1857323520
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.
90 : 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
53 : 1, 53
16 : 1, 2, 4, 8, 16
78 : 1, 2, 3, 6, 13, 26, 39, 78
312 : 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
1 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 90,53,16,78,312, is 1.
Now, the common factors can be found like this.
90:2x 3x 3x 5
53:53
16:2x 2x 2x 2
78:2x 3x 13
312:2x 2x 2x 3x 13
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 2x 3x 3x 13 = 3744
Therefore, the value for common factors is 3744.
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 = 1857323520/(1x3744)
LCM = 1857323520/3744
LCM = 496080
Thus, we can understand that the LCM of 90,53,16,78,312 is 496080.
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FAQs on LCM of 90, 53, 16, 78, 312
1. What is the LCM of 90, 53, 16, 78, 312?
Answer: LCM of 90, 53, 16, 78, 312 is 496080.
2. How to calculate the LCM of 90, 53, 16, 78, 312?
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 90, 53, 16, 78, 312.
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}.