LCM of 196, 978, 760, 810, 420
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 196, 978, 760, 810, 420 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 196, 978, 760, 810, 420. So, keep reading to learn more.
Given numbers are 196,978,760,810,420
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 196,978,760,810,420 is 491679720.
Find LCM of 196,978,760,810,420 with Prime Factorization
| 2 | 196, 978, 760, 810, 420 |
| 2 | 98, 489, 380, 405, 210 |
| 3 | 49, 489, 190, 405, 105 |
| 5 | 49, 163, 190, 135, 35 |
| 7 | 49, 163, 38, 27, 7 |
| 1, 163, 38, 27, 7 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 5 x 7 x 1 x 163 x 38 x 27 x 7 = 491679720
Therefore, the lowest common multiple of 196,978,760,810,420 is 491679720.
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.
196 x 978 x 760 x 810 x 420 = 49561315776000
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.
196 : 1, 2, 4, 7, 14, 28, 49, 98, 196
978 : 1, 2, 3, 6, 163, 326, 489, 978
760 : 1, 2, 4, 5, 8, 10, 19, 20, 38, 40, 76, 95, 152, 190, 380, 760
810 : 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405, 810
420 : 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
2 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 196,978,760,810,420, is 2.
Now, the common factors can be found like this.
196:2x 2x 7x 7
978:2x 3x 163
760:2x 2x 2x 5x 19
810:2x 3x 3x 3x 3x 5
420:2x 2x 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 2x 3x 3x 5x 5x 7 = 50400
Therefore, the value for common factors is 50400.
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 = 49561315776000/(2x50400)
LCM = 49561315776000/100800
LCM = 491679720
Thus, we can understand that the LCM of 196,978,760,810,420 is 491679720.
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FAQs on LCM of 196, 978, 760, 810, 420
1. What is the LCM of 196, 978, 760, 810, 420?
Answer: LCM of 196, 978, 760, 810, 420 is 491679720.
2. How to calculate the LCM of 196, 978, 760, 810, 420?
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 196, 978, 760, 810, 420.
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}.